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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 9025.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9025.d1 | 9025c3 | \([0, 1, 1, -6943233, 7039600194]\) | \(-50357871050752/19\) | \(-13966745921875\) | \([]\) | \(116640\) | \(2.3104\) | |
9025.d2 | 9025c2 | \([0, 1, 1, -84233, 9982569]\) | \(-89915392/6859\) | \(-5041995277796875\) | \([]\) | \(38880\) | \(1.7611\) | |
9025.d3 | 9025c1 | \([0, 1, 1, 6017, 9944]\) | \(32768/19\) | \(-13966745921875\) | \([]\) | \(12960\) | \(1.2118\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9025.d have rank \(0\).
Complex multiplication
The elliptic curves in class 9025.d do not have complex multiplication.Modular form 9025.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.