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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 392784i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
392784.i1 | 392784i1 | \([0, -1, 0, -247319, -47238666]\) | \(888770622281728/426952701\) | \(803688933119184\) | \([2]\) | \(2150400\) | \(1.8147\) | \(\Gamma_0(N)\)-optimal |
392784.i2 | 392784i2 | \([0, -1, 0, -206404, -63424640]\) | \(-32288802541648/39139035327\) | \(-1178795101999673088\) | \([2]\) | \(4300800\) | \(2.1613\) |
Rank
sage: E.rank()
The elliptic curves in class 392784i have rank \(0\).
Complex multiplication
The elliptic curves in class 392784i do not have complex multiplication.Modular form 392784.2.a.i
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.