Show commands:
SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 90160dg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 90160.s3 | 90160dg1 | \([0, 1, 0, -118400, 15186100]\) | \(380920459249/12622400\) | \(6082612173209600\) | \([2]\) | \(663552\) | \(1.8017\) | \(\Gamma_0(N)\)-optimal |
| 90160.s4 | 90160dg2 | \([0, 1, 0, 38400, 52629940]\) | \(12994449551/2489452840\) | \(-1199643185861263360\) | \([2]\) | \(1327104\) | \(2.1483\) | |
| 90160.s1 | 90160dg3 | \([0, 1, 0, -1325760, -582918092]\) | \(534774372149809/5323062500\) | \(2565132206336000000\) | \([2]\) | \(1990656\) | \(2.3510\) | |
| 90160.s2 | 90160dg4 | \([0, 1, 0, -345760, -1424542092]\) | \(-9486391169809/1813439640250\) | \(-873878979525723136000\) | \([2]\) | \(3981312\) | \(2.6976\) |
Rank
sage: E.rank()
The elliptic curves in class 90160dg have rank \(1\).
Complex multiplication
The elliptic curves in class 90160dg do not have complex multiplication.Modular form 90160.2.a.dg
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
