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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 279174z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
279174.z2 | 279174z1 | \([1, 0, 1, -4261167, 4141655074]\) | \(-354499561600764553/101902222098432\) | \(-2459671917154227191808\) | \([2]\) | \(20815872\) | \(2.8195\) | \(\Gamma_0(N)\)-optimal |
279174.z1 | 279174z2 | \([1, 0, 1, -72326447, 236734329890]\) | \(1733490909744055732873/99355964553216\) | \(2398211449964805371904\) | \([2]\) | \(41631744\) | \(3.1661\) |
Rank
sage: E.rank()
The elliptic curves in class 279174z have rank \(0\).
Complex multiplication
The elliptic curves in class 279174z do not have complex multiplication.Modular form 279174.2.a.z
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.