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SageMath
E = EllipticCurve("ma1")
E.isogeny_class()
Elliptic curves in class 221760ma
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
221760.s3 | 221760ma1 | \([0, 0, 0, -1494408, 703156232]\) | \(494428821070157824/77818125\) | \(58090919040000\) | \([2]\) | \(1966080\) | \(2.0448\) | \(\Gamma_0(N)\)-optimal |
221760.s2 | 221760ma2 | \([0, 0, 0, -1498908, 698708432]\) | \(31181799673942864/387562277025\) | \(4629019032800870400\) | \([2, 2]\) | \(3932160\) | \(2.3914\) | |
221760.s4 | 221760ma3 | \([0, 0, 0, -264108, 1815461552]\) | \(-42644293386916/29777663954115\) | \(-1422650049989825986560\) | \([2]\) | \(7864320\) | \(2.7380\) | |
221760.s1 | 221760ma4 | \([0, 0, 0, -2805708, -702703888]\) | \(51126217658776516/25121936269815\) | \(1200219196010996367360\) | \([2]\) | \(7864320\) | \(2.7380\) |
Rank
sage: E.rank()
The elliptic curves in class 221760ma have rank \(0\).
Complex multiplication
The elliptic curves in class 221760ma do not have complex multiplication.Modular form 221760.2.a.ma
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 Cremona 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 Cremona labels.