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SageMath
E = EllipticCurve("iz1")
E.isogeny_class()
Elliptic curves in class 114240.iz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 114240.iz1 | 114240jp7 | \([0, 1, 0, -851191425, 9551115581823]\) | \(260174968233082037895439009/223081361502731896500\) | \(58479440429772150276096000\) | \([2]\) | \(42467328\) | \(3.8709\) | |
| 114240.iz2 | 114240jp8 | \([0, 1, 0, -559031425, -5033746306177]\) | \(73704237235978088924479009/899277423164136103500\) | \(235740180817939294715904000\) | \([2]\) | \(42467328\) | \(3.8709\) | |
| 114240.iz3 | 114240jp5 | \([0, 1, 0, -557384065, -5065191475585]\) | \(73054578035931991395831649/136386452160\) | \(35752890115031040\) | \([2]\) | \(14155776\) | \(3.3216\) | |
| 114240.iz4 | 114240jp6 | \([0, 1, 0, -65111425, 77436637823]\) | \(116454264690812369959009/57505157319440250000\) | \(15074631960347344896000000\) | \([2, 2]\) | \(21233664\) | \(3.5244\) | |
| 114240.iz5 | 114240jp4 | \([0, 1, 0, -36577665, -70804859265]\) | \(20645800966247918737249/3688936444974392640\) | \(967032555431367184220160\) | \([2]\) | \(14155776\) | \(3.3216\) | |
| 114240.iz6 | 114240jp2 | \([0, 1, 0, -34836865, -79150602625]\) | \(17836145204788591940449/770635366502400\) | \(202017437516405145600\) | \([2, 2]\) | \(7077888\) | \(2.9751\) | |
| 114240.iz7 | 114240jp1 | \([0, 1, 0, -2068865, -1365924225]\) | \(-3735772816268612449/909650165760000\) | \(-238459333052989440000\) | \([2]\) | \(3538944\) | \(2.6285\) | \(\Gamma_0(N)\)-optimal |
| 114240.iz8 | 114240jp3 | \([0, 1, 0, 14888575, 9292637823]\) | \(1392333139184610040991/947901937500000000\) | \(-248486805504000000000000\) | \([2]\) | \(10616832\) | \(3.1778\) |
Rank
sage: E.rank()
The elliptic curves in class 114240.iz have rank \(0\).
Complex multiplication
The elliptic curves in class 114240.iz do not have complex multiplication.Modular form 114240.2.a.iz
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 12 & 2 & 3 & 6 & 12 & 4 \\ 4 & 1 & 3 & 2 & 12 & 6 & 12 & 4 \\ 12 & 3 & 1 & 6 & 4 & 2 & 4 & 12 \\ 2 & 2 & 6 & 1 & 6 & 3 & 6 & 2 \\ 3 & 12 & 4 & 6 & 1 & 2 & 4 & 12 \\ 6 & 6 & 2 & 3 & 2 & 1 & 2 & 6 \\ 12 & 12 & 4 & 6 & 4 & 2 & 1 & 3 \\ 4 & 4 & 12 & 2 & 12 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
