Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 296208.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 296208.d1 | 296208d1 | \([0, 0, 0, -3415467, 2427996890]\) | \(832972004929/610368\) | \(3228756874455416832\) | \([2]\) | \(8847360\) | \(2.4858\) | \(\Gamma_0(N)\)-optimal |
| 296208.d2 | 296208d2 | \([0, 0, 0, -2718507, 3447649370]\) | \(-420021471169/727634952\) | \(-3849081788960163790848\) | \([2]\) | \(17694720\) | \(2.8323\) |
Rank
sage: E.rank()
The elliptic curves in class 296208.d have rank \(2\).
Complex multiplication
The elliptic curves in class 296208.d do not have complex multiplication.Modular form 296208.2.a.d
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
