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SageMath
E = EllipticCurve("eq1")
E.isogeny_class()
Elliptic curves in class 458640eq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 458640.eq1 | 458640eq1 | \([0, 0, 0, -8668443, 4624536602]\) | \(820221748268836/369468094905\) | \(32448353621259994629120\) | \([2]\) | \(28901376\) | \(3.0148\) | \(\Gamma_0(N)\)-optimal |
| 458640.eq2 | 458640eq2 | \([0, 0, 0, 30086637, 34628719538]\) | \(17147425715207422/12872524043925\) | \(-2261046179280242411366400\) | \([2]\) | \(57802752\) | \(3.3613\) |
Rank
sage: E.rank()
The elliptic curves in class 458640eq have rank \(1\).
Complex multiplication
The elliptic curves in class 458640eq do not have complex multiplication.Modular form 458640.2.a.eq
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.
