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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 303450s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
303450.s2 | 303450s1 | \([1, 1, 0, 158800, 56577750]\) | \(46969655/173502\) | \(-1635904881499218750\) | \([]\) | \(4976640\) | \(2.1778\) | \(\Gamma_0(N)\)-optimal |
303450.s1 | 303450s2 | \([1, 1, 0, -1466825, -1765747875]\) | \(-37017366745/121331448\) | \(-1144002421081996875000\) | \([]\) | \(14929920\) | \(2.7271\) |
Rank
sage: E.rank()
The elliptic curves in class 303450s have rank \(0\).
Complex multiplication
The elliptic curves in class 303450s do not have complex multiplication.Modular form 303450.2.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.