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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 140790q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 140790.ck3 | 140790q1 | \([1, 0, 0, -4881, -127719]\) | \(273359449/9360\) | \(440349446160\) | \([2]\) | \(230400\) | \(1.0061\) | \(\Gamma_0(N)\)-optimal |
| 140790.ck2 | 140790q2 | \([1, 0, 0, -12101, 335805]\) | \(4165509529/1368900\) | \(64401106500900\) | \([2, 2]\) | \(460800\) | \(1.3527\) | |
| 140790.ck1 | 140790q3 | \([1, 0, 0, -174551, 28049775]\) | \(12501706118329/2570490\) | \(120930966651690\) | \([2]\) | \(921600\) | \(1.6993\) | |
| 140790.ck4 | 140790q4 | \([1, 0, 0, 34829, 2316251]\) | \(99317171591/106616250\) | \(-5015855410166250\) | \([2]\) | \(921600\) | \(1.6993\) |
Rank
sage: E.rank()
The elliptic curves in class 140790q have rank \(1\).
Complex multiplication
The elliptic curves in class 140790q do not have complex multiplication.Modular form 140790.2.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.
