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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 182070.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
182070.c1 | 182070dc2 | \([1, -1, 0, -45117000, 116661716500]\) | \(-6910788750049/514500\) | \(-756139840238356654500\) | \([]\) | \(16920576\) | \(3.0560\) | |
182070.c2 | 182070dc1 | \([1, -1, 0, -15660, 453603856]\) | \(-289/60480\) | \(-88885009791284374080\) | \([]\) | \(5640192\) | \(2.5067\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 182070.c have rank \(0\).
Complex multiplication
The elliptic curves in class 182070.c do not have complex multiplication.Modular form 182070.2.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.