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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 51714bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 51714.o2 | 51714bb1 | \([1, -1, 1, -1498217, -1017722455]\) | \(-48109395853/30081024\) | \(-232546771907307307008\) | \([2]\) | \(2875392\) | \(2.6096\) | \(\Gamma_0(N)\)-optimal |
| 51714.o1 | 51714bb2 | \([1, -1, 1, -26807657, -53408263255]\) | \(275602131611533/53934336\) | \(416949094943179898112\) | \([2]\) | \(5750784\) | \(2.9562\) |
Rank
sage: E.rank()
The elliptic curves in class 51714bb have rank \(0\).
Complex multiplication
The elliptic curves in class 51714bb do not have complex multiplication.Modular form 51714.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
