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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 44100.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44100.c1 | 44100bf1 | \([0, 0, 0, -224175, -40878250]\) | \(-177953104/125\) | \(-875164500000000\) | \([]\) | \(311040\) | \(1.8034\) | \(\Gamma_0(N)\)-optimal |
44100.c2 | 44100bf2 | \([0, 0, 0, 216825, -173619250]\) | \(161017136/1953125\) | \(-13674445312500000000\) | \([]\) | \(933120\) | \(2.3527\) |
Rank
sage: E.rank()
The elliptic curves in class 44100.c have rank \(1\).
Complex multiplication
The elliptic curves in class 44100.c do not have complex multiplication.Modular form 44100.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.