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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 47096e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 47096.l2 | 47096e1 | \([0, -1, 0, 63636, 7947668]\) | \(187153328/288463\) | \(-43925637029279488\) | \([2]\) | \(403200\) | \(1.8787\) | \(\Gamma_0(N)\)-optimal |
| 47096.l1 | 47096e2 | \([0, -1, 0, -424144, 80724444]\) | \(13854050788/3411821\) | \(2078137034626601984\) | \([2]\) | \(806400\) | \(2.2253\) |
Rank
sage: E.rank()
The elliptic curves in class 47096e have rank \(0\).
Complex multiplication
The elliptic curves in class 47096e do not have complex multiplication.Modular form 47096.2.a.e
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.
