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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 1275.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1275.d1 | 1275a2 | \([0, -1, 1, -1483, -21507]\) | \(-23100424192/14739\) | \(-230296875\) | \([]\) | \(648\) | \(0.54550\) | |
1275.d2 | 1275a1 | \([0, -1, 1, 17, -132]\) | \(32768/459\) | \(-7171875\) | \([]\) | \(216\) | \(-0.0038108\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1275.d have rank \(0\).
Complex multiplication
The elliptic curves in class 1275.d do not have complex multiplication.Modular form 1275.2.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.