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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 77616bz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
77616.e2 | 77616bz1 | \([0, 0, 0, -1481907, 828451330]\) | \(-4097989445764/1004475087\) | \(-88217530217602587648\) | \([2]\) | \(2949120\) | \(2.5455\) | \(\Gamma_0(N)\)-optimal |
77616.e1 | 77616bz2 | \([0, 0, 0, -24960747, 47997440890]\) | \(9791533777258802/427901859\) | \(75160540395763587072\) | \([2]\) | \(5898240\) | \(2.8921\) |
Rank
sage: E.rank()
The elliptic curves in class 77616bz have rank \(1\).
Complex multiplication
The elliptic curves in class 77616bz do not have complex multiplication.Modular form 77616.2.a.bz
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.