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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 5025.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5025.d1 | 5025a2 | \([0, -1, 1, -75033, -8712907]\) | \(-2989967081734144/380653171875\) | \(-5947705810546875\) | \([]\) | \(34560\) | \(1.7606\) | |
5025.d2 | 5025a1 | \([0, -1, 1, 5967, 24968]\) | \(1503484706816/890163675\) | \(-13908807421875\) | \([]\) | \(11520\) | \(1.2113\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5025.d have rank \(1\).
Complex multiplication
The elliptic curves in class 5025.d do not have complex multiplication.Modular form 5025.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.