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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 62790q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 62790.q3 | 62790q1 | \([1, 0, 1, -5883, -171194]\) | \(22512002790611881/439429536000\) | \(439429536000\) | \([2]\) | \(135168\) | \(1.0265\) | \(\Gamma_0(N)\)-optimal |
| 62790.q2 | 62790q2 | \([1, 0, 1, -12363, 272038]\) | \(208951176876460201/88708142250000\) | \(88708142250000\) | \([2, 2]\) | \(270336\) | \(1.3731\) | |
| 62790.q4 | 62790q3 | \([1, 0, 1, 41457, 2015806]\) | \(7880111917735501079/6309659179687500\) | \(-6309659179687500\) | \([2]\) | \(540672\) | \(1.7196\) | |
| 62790.q1 | 62790q4 | \([1, 0, 1, -169863, 26921038]\) | \(542021366615123140201/251764972231500\) | \(251764972231500\) | \([4]\) | \(540672\) | \(1.7196\) |
Rank
sage: E.rank()
The elliptic curves in class 62790q have rank \(1\).
Complex multiplication
The elliptic curves in class 62790q do not have complex multiplication.Modular form 62790.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
