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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 2310.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2310.s1 | 2310s1 | \([1, 0, 0, -6, 0]\) | \(24137569/13860\) | \(13860\) | \([2]\) | \(192\) | \(-0.51563\) | \(\Gamma_0(N)\)-optimal |
2310.s2 | 2310s2 | \([1, 0, 0, 24, 6]\) | \(1524845951/889350\) | \(-889350\) | \([2]\) | \(384\) | \(-0.16905\) |
Rank
sage: E.rank()
The elliptic curves in class 2310.s have rank \(0\).
Complex multiplication
The elliptic curves in class 2310.s do not have complex multiplication.Modular form 2310.2.a.s
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.