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SageMath
E = EllipticCurve("cz1")
E.isogeny_class()
Elliptic curves in class 374850cz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
374850.cz2 | 374850cz1 | \([1, -1, 0, -18560817, -80479938659]\) | \(-527690404915129/1782829440000\) | \(-2389161960521910000000000\) | \([2]\) | \(70778880\) | \(3.3639\) | \(\Gamma_0(N)\)-optimal |
374850.cz1 | 374850cz2 | \([1, -1, 0, -415460817, -3255283038659]\) | \(5918043195362419129/8515734343200\) | \(11411898470042917612500000\) | \([2]\) | \(141557760\) | \(3.7105\) |
Rank
sage: E.rank()
The elliptic curves in class 374850cz have rank \(0\).
Complex multiplication
The elliptic curves in class 374850cz do not have complex multiplication.Modular form 374850.2.a.cz
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.