Show commands:
SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 296208w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 296208.w3 | 296208w1 | \([0, 0, 0, -56991, -5225506]\) | \(61918288/153\) | \(50584217409792\) | \([2]\) | \(1310720\) | \(1.5074\) | \(\Gamma_0(N)\)-optimal |
| 296208.w2 | 296208w2 | \([0, 0, 0, -78771, -865150]\) | \(40873252/23409\) | \(30957541054792704\) | \([2, 2]\) | \(2621440\) | \(1.8540\) | |
| 296208.w1 | 296208w3 | \([0, 0, 0, -819291, 284235050]\) | \(22994537186/111537\) | \(295007155933906944\) | \([2]\) | \(5242880\) | \(2.2006\) | |
| 296208.w4 | 296208w4 | \([0, 0, 0, 313269, -6902566]\) | \(1285471294/751689\) | \(-1988162081074464768\) | \([2]\) | \(5242880\) | \(2.2006\) |
Rank
sage: E.rank()
The elliptic curves in class 296208w have rank \(2\).
Complex multiplication
The elliptic curves in class 296208w do not have complex multiplication.Modular form 296208.2.a.w
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
