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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 30096p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30096.bj2 | 30096p1 | \([0, 0, 0, 549, 11402]\) | \(165469149/603592\) | \(-66752446464\) | \([]\) | \(34560\) | \(0.75991\) | \(\Gamma_0(N)\)-optimal |
| 30096.bj1 | 30096p2 | \([0, 0, 0, -26811, 1692522]\) | \(-26436959739/50578\) | \(-4077677666304\) | \([]\) | \(103680\) | \(1.3092\) |
Rank
sage: E.rank()
The elliptic curves in class 30096p have rank \(1\).
Complex multiplication
The elliptic curves in class 30096p do not have complex multiplication.Modular form 30096.2.a.p
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
