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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 86490.cc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
86490.cc1 | 86490ce2 | \([1, -1, 1, -323840363, 2092571438267]\) | \(5805223604235668521/435937500000000\) | \(282047283097298437500000000\) | \([2]\) | \(41287680\) | \(3.8207\) | |
86490.cc2 | 86490ce1 | \([1, -1, 1, 19351957, 145023660731]\) | \(1238798620042199/14760960000000\) | \(-9550196218283351040000000\) | \([2]\) | \(20643840\) | \(3.4741\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 86490.cc have rank \(0\).
Complex multiplication
The elliptic curves in class 86490.cc do not have complex multiplication.Modular form 86490.2.a.cc
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.