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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 570.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
570.c1 | 570c2 | \([1, 1, 0, -397, 2881]\) | \(6947097508441/10687500\) | \(10687500\) | \([2]\) | \(192\) | \(0.24807\) | |
570.c2 | 570c1 | \([1, 1, 0, -17, 69]\) | \(-594823321/2166000\) | \(-2166000\) | \([2]\) | \(96\) | \(-0.098508\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 570.c have rank \(1\).
Complex multiplication
The elliptic curves in class 570.c do not have complex multiplication.Modular form 570.2.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.