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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 95304p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
95304.n1 | 95304p1 | \([0, -1, 0, -2893896, 1895804028]\) | \(55635379958596/24057\) | \(1158945545438208\) | \([2]\) | \(2322432\) | \(2.2329\) | \(\Gamma_0(N)\)-optimal |
95304.n2 | 95304p2 | \([0, -1, 0, -2879456, 1915644588]\) | \(-27403349188178/578739249\) | \(-55761505973213939712\) | \([2]\) | \(4644864\) | \(2.5795\) |
Rank
sage: E.rank()
The elliptic curves in class 95304p have rank \(1\).
Complex multiplication
The elliptic curves in class 95304p do not have complex multiplication.Modular form 95304.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.