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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 11550e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11550.e2 | 11550e1 | \([1, 1, 0, 48305, 993445]\) | \(498592699047570335/304907615857152\) | \(-7622690396428800\) | \([]\) | \(116640\) | \(1.7367\) | \(\Gamma_0(N)\)-optimal |
| 11550.e1 | 11550e2 | \([1, 1, 0, -583495, -193824515]\) | \(-878812616455788778465/138974375664304488\) | \(-3474359391607612200\) | \([]\) | \(349920\) | \(2.2860\) |
Rank
sage: E.rank()
The elliptic curves in class 11550e have rank \(1\).
Complex multiplication
The elliptic curves in class 11550e do not have complex multiplication.Modular form 11550.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
