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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 2275.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2275.d1 | 2275a3 | \([0, -1, 1, -2933, -149732]\) | \(-178643795968/524596891\) | \(-8196826421875\) | \([]\) | \(3888\) | \(1.1648\) | |
| 2275.d2 | 2275a1 | \([0, -1, 1, -183, 1018]\) | \(-43614208/91\) | \(-1421875\) | \([]\) | \(432\) | \(0.066211\) | \(\Gamma_0(N)\)-optimal |
| 2275.d3 | 2275a2 | \([0, -1, 1, 317, 4643]\) | \(224755712/753571\) | \(-11774546875\) | \([]\) | \(1296\) | \(0.61552\) |
Rank
sage: E.rank()
The elliptic curves in class 2275.d have rank \(1\).
Complex multiplication
The elliptic curves in class 2275.d do not have complex multiplication.Modular form 2275.2.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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
