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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 76440bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76440.cg2 | 76440bc1 | \([0, 1, 0, 35264, 2707760]\) | \(40254822716/49359375\) | \(-5946451056000000\) | \([2]\) | \(345600\) | \(1.7129\) | \(\Gamma_0(N)\)-optimal |
| 76440.cg1 | 76440bc2 | \([0, 1, 0, -209736, 25835760]\) | \(4234737878642/1247410125\) | \(300557422174464000\) | \([2]\) | \(691200\) | \(2.0595\) |
Rank
sage: E.rank()
The elliptic curves in class 76440bc have rank \(0\).
Complex multiplication
The elliptic curves in class 76440bc do not have complex multiplication.Modular form 76440.2.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 Cremona 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 Cremona labels.
