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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 3570.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3570.d1 | 3570f2 | \([1, 1, 0, -40957, -3207491]\) | \(7598444481718798681/108756480\) | \(108756480\) | \([2]\) | \(9216\) | \(1.0951\) | |
3570.d2 | 3570f1 | \([1, 1, 0, -2557, -51011]\) | \(-1850040570997081/7018905600\) | \(-7018905600\) | \([2]\) | \(4608\) | \(0.74853\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3570.d have rank \(1\).
Complex multiplication
The elliptic curves in class 3570.d do not have complex multiplication.Modular form 3570.2.a.d
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.