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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1856.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1856.c1 | 1856e1 | \([0, 1, 0, -37, 75]\) | \(5619712/29\) | \(29696\) | \([2]\) | \(240\) | \(-0.29599\) | \(\Gamma_0(N)\)-optimal |
1856.c2 | 1856e2 | \([0, 1, 0, -17, 175]\) | \(-35152/841\) | \(-13778944\) | \([2]\) | \(480\) | \(0.050583\) |
Rank
sage: E.rank()
The elliptic curves in class 1856.c have rank \(0\).
Complex multiplication
The elliptic curves in class 1856.c do not have complex multiplication.Modular form 1856.2.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.