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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 381150s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
381150.s2 | 381150s1 | \([1, -1, 0, -5425602, -5345734124]\) | \(-1787281834251393315/215504279044096\) | \(-2129758750902111436800\) | \([]\) | \(23224320\) | \(2.8278\) | \(\Gamma_0(N)\)-optimal |
381150.s1 | 381150s2 | \([1, -1, 0, -451480002, -3692262895084]\) | \(-1412658626195854329435/1927561216\) | \(-13887057098402611200\) | \([]\) | \(69672960\) | \(3.3771\) |
Rank
sage: E.rank()
The elliptic curves in class 381150s have rank \(0\).
Complex multiplication
The elliptic curves in class 381150s do not have complex multiplication.Modular form 381150.2.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.