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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 20475q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20475.r2 | 20475q1 | \([0, 0, 1, -1650, -25844]\) | \(-43614208/91\) | \(-1036546875\) | \([]\) | \(10368\) | \(0.61552\) | \(\Gamma_0(N)\)-optimal |
| 20475.r3 | 20475q2 | \([0, 0, 1, 2850, -128219]\) | \(224755712/753571\) | \(-8583644671875\) | \([]\) | \(31104\) | \(1.1648\) | |
| 20475.r1 | 20475q3 | \([0, 0, 1, -26400, 4069156]\) | \(-178643795968/524596891\) | \(-5975486461546875\) | \([]\) | \(93312\) | \(1.7141\) |
Rank
sage: E.rank()
The elliptic curves in class 20475q have rank \(0\).
Complex multiplication
The elliptic curves in class 20475q do not have complex multiplication.Modular form 20475.2.a.q
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.
