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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 324870s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
324870.s2 | 324870s1 | \([1, 1, 0, -7977582, -7984739916]\) | \(1145886354864987091635769/101502227356009758720\) | \(4973609140444478177280\) | \([]\) | \(27319680\) | \(2.9033\) | \(\Gamma_0(N)\)-optimal |
324870.s1 | 324870s2 | \([1, 1, 0, -133911117, 594953824221]\) | \(5419728549194533398573442729/15116050674292359168000\) | \(740686483040325599232000\) | \([]\) | \(81959040\) | \(3.4526\) |
Rank
sage: E.rank()
The elliptic curves in class 324870s have rank \(1\).
Complex multiplication
The elliptic curves in class 324870s do not have complex multiplication.Modular form 324870.2.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 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.