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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 418950.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
418950.c1 | 418950c1 | \([1, -1, 0, -370404758817, 86365418852201341]\) | \(4193895363953824558241038009/22511668914990297907200\) | \(30167789376171821939608780800000000\) | \([2]\) | \(7060193280\) | \(5.4601\) | \(\Gamma_0(N)\)-optimal |
418950.c2 | 418950c2 | \([1, -1, 0, -168095126817, 180295150964585341]\) | \(-391970413583429733188386489/10252068819290850263040000\) | \(-13738752732119159341449538560000000000\) | \([2]\) | \(14120386560\) | \(5.8067\) |
Rank
sage: E.rank()
The elliptic curves in class 418950.c have rank \(0\).
Complex multiplication
The elliptic curves in class 418950.c do not have complex multiplication.Modular form 418950.2.a.c
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.