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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 42432.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 42432.t1 | 42432g1 | \([0, -1, 0, -113217, -5215167]\) | \(612241204436497/308834353152\) | \(80959072672677888\) | \([2]\) | \(344064\) | \(1.9370\) | \(\Gamma_0(N)\)-optimal |
| 42432.t2 | 42432g2 | \([0, -1, 0, 419263, -40678335]\) | \(31091549545392623/20700995942016\) | \(-5426641880223842304\) | \([2]\) | \(688128\) | \(2.2836\) |
Rank
sage: E.rank()
The elliptic curves in class 42432.t have rank \(0\).
Complex multiplication
The elliptic curves in class 42432.t do not have complex multiplication.Modular form 42432.2.a.t
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.
