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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 8624bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8624.s1 | 8624bb1 | \([0, 1, 0, -70037, 7110851]\) | \(-78843215872/539\) | \(-259738873856\) | \([]\) | \(23040\) | \(1.3711\) | \(\Gamma_0(N)\)-optimal |
| 8624.s2 | 8624bb2 | \([0, 1, 0, -38677, 13523971]\) | \(-13278380032/156590819\) | \(-75459597371518976\) | \([]\) | \(69120\) | \(1.9204\) | |
| 8624.s3 | 8624bb3 | \([0, 1, 0, 345483, -350275549]\) | \(9463555063808/115539436859\) | \(-55677334351972315136\) | \([]\) | \(207360\) | \(2.4697\) |
Rank
sage: E.rank()
The elliptic curves in class 8624bb have rank \(0\).
Complex multiplication
The elliptic curves in class 8624bb do not have complex multiplication.Modular form 8624.2.a.bb
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
