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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 366275r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 366275.r3 | 366275r1 | \([0, 1, 1, 19858067, -36487108206]\) | \(471114356703100928/585612268875179\) | \(-1076510903451498971421875\) | \([]\) | \(40310784\) | \(3.2974\) | \(\Gamma_0(N)\)-optimal |
| 366275.r2 | 366275r2 | \([0, 1, 1, -195447933, 1637153712919]\) | \(-449167881463536812032/369990050199923699\) | \(-680139990874544113494546875\) | \([]\) | \(120932352\) | \(3.8467\) | |
| 366275.r1 | 366275r3 | \([0, 1, 1, -18166332683, 942423867614044]\) | \(-360675992659311050823073792/56219378022244619\) | \(-103346150077172768448921875\) | \([]\) | \(362797056\) | \(4.3960\) |
Rank
sage: E.rank()
The elliptic curves in class 366275r have rank \(2\).
Complex multiplication
The elliptic curves in class 366275r do not have complex multiplication.Modular form 366275.2.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 Cremona 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 Cremona labels.
