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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 28665.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28665.bd1 | 28665l2 | \([0, 0, 1, -18522, 974720]\) | \(-303464448/1625\) | \(-3762988558875\) | \([]\) | \(54432\) | \(1.2575\) | |
| 28665.bd2 | 28665l1 | \([0, 0, 1, 588, 7117]\) | \(7077888/10985\) | \(-34894105155\) | \([]\) | \(18144\) | \(0.70824\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 28665.bd have rank \(1\).
Complex multiplication
The elliptic curves in class 28665.bd do not have complex multiplication.Modular form 28665.2.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 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.
