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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 366275s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
366275.s1 | 366275s1 | \([0, 1, 1, -53516983, -150708228681]\) | \(-9221261135586623488/121324931\) | \(-223027450112796875\) | \([]\) | \(17915904\) | \(2.8872\) | \(\Gamma_0(N)\)-optimal |
366275.s2 | 366275s2 | \([0, 1, 1, -50491233, -168497329556]\) | \(-7743965038771437568/2189290237869371\) | \(-4024496987423337949671875\) | \([]\) | \(53747712\) | \(3.4365\) |
Rank
sage: E.rank()
The elliptic curves in class 366275s have rank \(0\).
Complex multiplication
The elliptic curves in class 366275s do not have complex multiplication.Modular form 366275.2.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.