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SageMath
E = EllipticCurve("qv1")
E.isogeny_class()
Elliptic curves in class 369600qv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.qv4 | 369600qv1 | \([0, 1, 0, 6467, -359437]\) | \(1869154304/4611915\) | \(-73790640000000\) | \([2]\) | \(1179648\) | \(1.3449\) | \(\Gamma_0(N)\)-optimal |
| 369600.qv3 | 369600qv2 | \([0, 1, 0, -54033, -4049937]\) | \(68150496976/12006225\) | \(3073593600000000\) | \([2, 2]\) | \(2359296\) | \(1.6915\) | |
| 369600.qv2 | 369600qv3 | \([0, 1, 0, -252033, 44856063]\) | \(1729010797924/148561875\) | \(152127360000000000\) | \([2]\) | \(4718592\) | \(2.0380\) | |
| 369600.qv1 | 369600qv4 | \([0, 1, 0, -824033, -288179937]\) | \(60430765429444/2525985\) | \(2586608640000000\) | \([2]\) | \(4718592\) | \(2.0380\) |
Rank
sage: E.rank()
The elliptic curves in class 369600qv have rank \(0\).
Complex multiplication
The elliptic curves in class 369600qv do not have complex multiplication.Modular form 369600.2.a.qv
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.
