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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 10320bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10320.bb2 | 10320bd1 | \([0, 1, 0, -164096, 26476980]\) | \(-119305480789133569/5200091136000\) | \(-21299573293056000\) | \([2]\) | \(120960\) | \(1.8986\) | \(\Gamma_0(N)\)-optimal |
| 10320.bb1 | 10320bd2 | \([0, 1, 0, -2652416, 1661800884]\) | \(503835593418244309249/898614000000\) | \(3680722944000000\) | \([2]\) | \(241920\) | \(2.2451\) |
Rank
sage: E.rank()
The elliptic curves in class 10320bd have rank \(0\).
Complex multiplication
The elliptic curves in class 10320bd do not have complex multiplication.Modular form 10320.2.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.
