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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 1350.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1350.r1 | 1350m3 | \([1, -1, 1, -3080, -86453]\) | \(-1167051/512\) | \(-1417176000000\) | \([]\) | \(1944\) | \(1.0388\) | |
1350.r2 | 1350m1 | \([1, -1, 1, -80, 297]\) | \(-132651/2\) | \(-843750\) | \([]\) | \(216\) | \(-0.059792\) | \(\Gamma_0(N)\)-optimal |
1350.r3 | 1350m2 | \([1, -1, 1, 295, 1297]\) | \(9261/8\) | \(-2460375000\) | \([]\) | \(648\) | \(0.48951\) |
Rank
sage: E.rank()
The elliptic curves in class 1350.r have rank \(0\).
Complex multiplication
The elliptic curves in class 1350.r do not have complex multiplication.Modular form 1350.2.a.r
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.