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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 15895d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15895.d1 | 15895d1 | \([0, -1, 1, -3801891, 2854572247]\) | \(-251784668965666816/353546875\) | \(-8533762090046875\) | \([]\) | \(421632\) | \(2.3292\) | \(\Gamma_0(N)\)-optimal |
15895.d2 | 15895d2 | \([0, -1, 1, -2790391, 4405555772]\) | \(-99546392709922816/289614925147075\) | \(-6990600239167357960675\) | \([]\) | \(1264896\) | \(2.8785\) |
Rank
sage: E.rank()
The elliptic curves in class 15895d have rank \(2\).
Complex multiplication
The elliptic curves in class 15895d do not have complex multiplication.Modular form 15895.2.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 Cremona 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 Cremona labels.