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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 176505s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
176505.r3 | 176505s1 | \([1, 1, 0, -4237, 98824]\) | \(1771561/105\) | \(498760945305\) | \([2]\) | \(276480\) | \(0.99768\) | \(\Gamma_0(N)\)-optimal |
176505.r2 | 176505s2 | \([1, 1, 0, -12642, -427329]\) | \(47045881/11025\) | \(52369899257025\) | \([2, 2]\) | \(552960\) | \(1.3442\) | |
176505.r4 | 176505s3 | \([1, 1, 0, 29383, -2621034]\) | \(590589719/972405\) | \(-4619025114469605\) | \([2]\) | \(1105920\) | \(1.6908\) | |
176505.r1 | 176505s4 | \([1, 1, 0, -189147, -31739316]\) | \(157551496201/13125\) | \(62345118163125\) | \([2]\) | \(1105920\) | \(1.6908\) |
Rank
sage: E.rank()
The elliptic curves in class 176505s have rank \(0\).
Complex multiplication
The elliptic curves in class 176505s do not have complex multiplication.Modular form 176505.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.