Show commands:
SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 37440e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37440.f3 | 37440e1 | \([0, 0, 0, -15948, 783728]\) | \(-63378025803/812500\) | \(-5750784000000\) | \([2]\) | \(110592\) | \(1.2576\) | \(\Gamma_0(N)\)-optimal |
| 37440.f2 | 37440e2 | \([0, 0, 0, -255948, 49839728]\) | \(261984288445803/42250\) | \(299040768000\) | \([2]\) | \(221184\) | \(1.6042\) | |
| 37440.f4 | 37440e3 | \([0, 0, 0, 56052, 3986928]\) | \(3774555693/3515200\) | \(-18137659893350400\) | \([2]\) | \(331776\) | \(1.8070\) | |
| 37440.f1 | 37440e4 | \([0, 0, 0, -289548, 35920368]\) | \(520300455507/193072360\) | \(996210969642270720\) | \([2]\) | \(663552\) | \(2.1535\) |
Rank
sage: E.rank()
The elliptic curves in class 37440e have rank \(1\).
Complex multiplication
The elliptic curves in class 37440e do not have complex multiplication.Modular form 37440.2.a.e
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
