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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 50400.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 50400.a1 | 50400eg1 | \([0, 0, 0, -1245, 16900]\) | \(36594368/21\) | \(122472000\) | \([2]\) | \(32768\) | \(0.49796\) | \(\Gamma_0(N)\)-optimal |
| 50400.a2 | 50400eg2 | \([0, 0, 0, -1020, 23200]\) | \(-314432/441\) | \(-164602368000\) | \([2]\) | \(65536\) | \(0.84454\) |
Rank
sage: E.rank()
The elliptic curves in class 50400.a have rank \(2\).
Complex multiplication
The elliptic curves in class 50400.a do not have complex multiplication.Modular form 50400.2.a.a
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
