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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 2310.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2310.p1 | 2310p1 | \([1, 1, 1, -4995, -137955]\) | \(13782741913468081/701662500\) | \(701662500\) | \([2]\) | \(2880\) | \(0.76742\) | \(\Gamma_0(N)\)-optimal |
2310.p2 | 2310p2 | \([1, 1, 1, -4725, -153183]\) | \(-11666347147400401/3126621093750\) | \(-3126621093750\) | \([2]\) | \(5760\) | \(1.1140\) |
Rank
sage: E.rank()
The elliptic curves in class 2310.p have rank \(0\).
Complex multiplication
The elliptic curves in class 2310.p do not have complex multiplication.Modular form 2310.2.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 LMFDB 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 LMFDB labels.