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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 19600.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19600.bc1 | 19600cm1 | \([0, -1, 0, -1220508, 519712012]\) | \(-177953104/125\) | \(-141237624500000000\) | \([]\) | \(290304\) | \(2.2271\) | \(\Gamma_0(N)\)-optimal |
| 19600.bc2 | 19600cm2 | \([0, -1, 0, 1180492, 2205214012]\) | \(161017136/1953125\) | \(-2206837882812500000000\) | \([]\) | \(870912\) | \(2.7764\) |
Rank
sage: E.rank()
The elliptic curves in class 19600.bc have rank \(1\).
Complex multiplication
The elliptic curves in class 19600.bc do not have complex multiplication.Modular form 19600.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
