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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 42432e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 42432.bc1 | 42432e1 | \([0, -1, 0, -4997, 137637]\) | \(13478411517952/304317\) | \(311620608\) | \([2]\) | \(30720\) | \(0.74390\) | \(\Gamma_0(N)\)-optimal |
| 42432.bc2 | 42432e2 | \([0, -1, 0, -4817, 147825]\) | \(-754612278352/127035441\) | \(-2081348665344\) | \([2]\) | \(61440\) | \(1.0905\) |
Rank
sage: E.rank()
The elliptic curves in class 42432e have rank \(0\).
Complex multiplication
The elliptic curves in class 42432e do not have complex multiplication.Modular form 42432.2.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.
