Show commands:
SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 212940bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 212940.d2 | 212940bd1 | \([0, 0, 0, 312, 43108]\) | \(106496/25515\) | \(-804729219840\) | \([]\) | \(248832\) | \(0.96368\) | \(\Gamma_0(N)\)-optimal |
| 212940.d1 | 212940bd2 | \([0, 0, 0, -83928, 9360052]\) | \(-2072956248064/385875\) | \(-12170287584000\) | \([]\) | \(746496\) | \(1.5130\) |
Rank
sage: E.rank()
The elliptic curves in class 212940bd have rank \(1\).
Complex multiplication
The elliptic curves in class 212940bd do not have complex multiplication.Modular form 212940.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
