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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 3570.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3570.c1 | 3570c2 | \([1, 1, 0, -518, 3132]\) | \(15417797707369/4080067320\) | \(4080067320\) | \([2]\) | \(2304\) | \(0.55269\) | |
3570.c2 | 3570c1 | \([1, 1, 0, 82, 372]\) | \(59822347031/83966400\) | \(-83966400\) | \([2]\) | \(1152\) | \(0.20612\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3570.c have rank \(1\).
Complex multiplication
The elliptic curves in class 3570.c do not have complex multiplication.Modular form 3570.2.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.