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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 296208bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 296208.bd2 | 296208bd1 | \([0, 0, 0, -4609011, 188264626]\) | \(2046931732873/1181672448\) | \(6250873308945686986752\) | \([2]\) | \(11059200\) | \(2.8718\) | \(\Gamma_0(N)\)-optimal |
| 296208.bd1 | 296208bd2 | \([0, 0, 0, -52002291, 143969997490]\) | \(2940001530995593/8673562656\) | \(45881869710698764959744\) | \([2]\) | \(22118400\) | \(3.2183\) |
Rank
sage: E.rank()
The elliptic curves in class 296208bd have rank \(0\).
Complex multiplication
The elliptic curves in class 296208bd do not have complex multiplication.Modular form 296208.2.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.
