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SageMath
E = EllipticCurve("jg1")
E.isogeny_class()
Elliptic curves in class 323400.jg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 323400.jg1 | 323400jg1 | \([0, 1, 0, -5443083, -4889524662]\) | \(4850878539776/130977\) | \(481541033531250000\) | \([2]\) | \(7987200\) | \(2.4973\) | \(\Gamma_0(N)\)-optimal |
| 323400.jg2 | 323400jg2 | \([0, 1, 0, -5228708, -5292120912]\) | \(-268750151696/50014503\) | \(-2942078131723500000000\) | \([2]\) | \(15974400\) | \(2.8439\) |
Rank
sage: E.rank()
The elliptic curves in class 323400.jg have rank \(1\).
Complex multiplication
The elliptic curves in class 323400.jg do not have complex multiplication.Modular form 323400.2.a.jg
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 LMFDB 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 LMFDB labels.
