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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 254320.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 254320.bc1 | 254320bc1 | \([0, 0, 0, -10982, 427431]\) | \(379275264/15125\) | \(5841291698000\) | \([2]\) | \(497664\) | \(1.2162\) | \(\Gamma_0(N)\)-optimal |
| 254320.bc2 | 254320bc2 | \([0, 0, 0, 4913, 1562334]\) | \(2122416/171875\) | \(-1062053036000000\) | \([2]\) | \(995328\) | \(1.5628\) |
Rank
sage: E.rank()
The elliptic curves in class 254320.bc have rank \(0\).
Complex multiplication
The elliptic curves in class 254320.bc do not have complex multiplication.Modular form 254320.2.a.bc
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.
