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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 71478y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
71478.q2 | 71478y1 | \([1, -1, 0, -17082, -1055480]\) | \(-2094688437625/631351908\) | \(-166152250276452\) | \([]\) | \(207360\) | \(1.4427\) | \(\Gamma_0(N)\)-optimal |
71478.q1 | 71478y2 | \([1, -1, 0, -1471437, -686638427]\) | \(-1338795256993539625/20699712\) | \(-5447522507328\) | \([]\) | \(622080\) | \(1.9920\) |
Rank
sage: E.rank()
The elliptic curves in class 71478y have rank \(0\).
Complex multiplication
The elliptic curves in class 71478y do not have complex multiplication.Modular form 71478.2.a.y
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.