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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 76230q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76230.k3 | 76230q1 | \([1, -1, 0, -84420, -9278384]\) | \(51520374361/887040\) | \(1145583747221760\) | \([2]\) | \(491520\) | \(1.6867\) | \(\Gamma_0(N)\)-optimal |
| 76230.k2 | 76230q2 | \([1, -1, 0, -171540, 13216000]\) | \(432252699481/192099600\) | \(248090480257712400\) | \([2, 2]\) | \(983040\) | \(2.0333\) | |
| 76230.k4 | 76230q3 | \([1, -1, 0, 590760, 98136220]\) | \(17655210697319/13448344140\) | \(-17368105692898851660\) | \([2]\) | \(1966080\) | \(2.3799\) | |
| 76230.k1 | 76230q4 | \([1, -1, 0, -2327760, 1366890916]\) | \(1080077156587801/594247500\) | \(767451611908327500\) | \([2]\) | \(1966080\) | \(2.3799\) |
Rank
sage: E.rank()
The elliptic curves in class 76230q have rank \(1\).
Complex multiplication
The elliptic curves in class 76230q do not have complex multiplication.Modular form 76230.2.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.
