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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 300560bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 300560.bd1 | 300560bd1 | \([0, 0, 0, -81787, -4038486]\) | \(611960049/282880\) | \(27967633484677120\) | \([2]\) | \(1769472\) | \(1.8505\) | \(\Gamma_0(N)\)-optimal |
| 300560.bd2 | 300560bd2 | \([0, 0, 0, 288133, -30450774]\) | \(26757728271/19536400\) | \(-1931514687535513600\) | \([2]\) | \(3538944\) | \(2.1971\) |
Rank
sage: E.rank()
The elliptic curves in class 300560bd have rank \(1\).
Complex multiplication
The elliptic curves in class 300560bd do not have complex multiplication.Modular form 300560.2.a.bd
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.
