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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 277350.cc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
277350.cc1 | 277350cc2 | \([1, 1, 1, -82281463, -336138727219]\) | \(-337335507529/72000000\) | \(-13149225312301125000000000\) | \([]\) | \(74898432\) | \(3.5412\) | |
277350.cc2 | 277350cc1 | \([1, 1, 1, 7163912, 2680353281]\) | \(222641831/145800\) | \(-26627181257409778125000\) | \([]\) | \(24966144\) | \(2.9919\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 277350.cc have rank \(0\).
Complex multiplication
The elliptic curves in class 277350.cc do not have complex multiplication.Modular form 277350.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.