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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 185020.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
185020.d1 | 185020d2 | \([0, 1, 0, -50740, 4371300]\) | \(94875856/275\) | \(41875561798400\) | \([2]\) | \(602112\) | \(1.4846\) | |
185020.d2 | 185020d1 | \([0, 1, 0, -4485, 4828]\) | \(1048576/605\) | \(5757889747280\) | \([2]\) | \(301056\) | \(1.1380\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 185020.d have rank \(1\).
Complex multiplication
The elliptic curves in class 185020.d do not have complex multiplication.Modular form 185020.2.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.