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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 19950.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19950.d1 | 19950j2 | \([1, 1, 0, -81375, -7234875]\) | \(3814038123905521/773540010432\) | \(12086562663000000\) | \([2]\) | \(215040\) | \(1.8016\) | |
19950.d2 | 19950j1 | \([1, 1, 0, -25375, 1445125]\) | \(115650783909361/8339853312\) | \(130310208000000\) | \([2]\) | \(107520\) | \(1.4551\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 19950.d have rank \(0\).
Complex multiplication
The elliptic curves in class 19950.d do not have complex multiplication.Modular form 19950.2.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.