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SageMath
E = EllipticCurve("it1")
E.isogeny_class()
Elliptic curves in class 141120.it
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141120.it1 | 141120e4 | \([0, 0, 0, -39330732, 58788240784]\) | \(2394165105226952/854262178245\) | \(2400804973611720299151360\) | \([2]\) | \(23592960\) | \(3.3791\) | |
| 141120.it2 | 141120e2 | \([0, 0, 0, -35008932, 79710938944]\) | \(13507798771700416/3544416225\) | \(1245146443070313369600\) | \([2, 2]\) | \(11796480\) | \(3.0325\) | |
| 141120.it3 | 141120e1 | \([0, 0, 0, -35006727, 79721484136]\) | \(864335783029582144/59535\) | \(326789504879040\) | \([2]\) | \(5898240\) | \(2.6859\) | \(\Gamma_0(N)\)-optimal |
| 141120.it4 | 141120e3 | \([0, 0, 0, -30722412, 99958744816]\) | \(-1141100604753992/875529151875\) | \(-2460573341408907325440000\) | \([2]\) | \(23592960\) | \(3.3791\) |
Rank
sage: E.rank()
The elliptic curves in class 141120.it have rank \(1\).
Complex multiplication
The elliptic curves in class 141120.it do not have complex multiplication.Modular form 141120.2.a.it
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
