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SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 284592cj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
284592.cj2 | 284592cj1 | \([0, -1, 0, -1976, -77328]\) | \(-2401/6\) | \(-2133356273664\) | \([]\) | \(342720\) | \(1.0536\) | \(\Gamma_0(N)\)-optimal |
284592.cj1 | 284592cj2 | \([0, -1, 0, -273016, 57057904]\) | \(-6329617441/279936\) | \(-99533870304067584\) | \([]\) | \(2399040\) | \(2.0266\) |
Rank
sage: E.rank()
The elliptic curves in class 284592cj have rank \(0\).
Complex multiplication
The elliptic curves in class 284592cj do not have complex multiplication.Modular form 284592.2.a.cj
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.