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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 363726q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 363726.q2 | 363726q1 | \([1, -1, 0, -1737522, -1434774060]\) | \(-449191107501625/429068648448\) | \(-554128415972713562112\) | \([2]\) | \(9953280\) | \(2.6766\) | \(\Gamma_0(N)\)-optimal |
| 363726.q1 | 363726q2 | \([1, -1, 0, -32403762, -70967406636]\) | \(2913576204142509625/1030541833728\) | \(1330911768974235858432\) | \([2]\) | \(19906560\) | \(3.0231\) |
Rank
sage: E.rank()
The elliptic curves in class 363726q have rank \(1\).
Complex multiplication
The elliptic curves in class 363726q do not have complex multiplication.Modular form 363726.2.a.q
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.
