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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 5082.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5082.v1 | 5082u3 | \([1, 1, 1, -11132547, -14301472767]\) | \(86129359107301290313/9166294368\) | \(16238649616868448\) | \([2]\) | \(230400\) | \(2.5383\) | |
| 5082.v2 | 5082u2 | \([1, 1, 1, -697507, -222516799]\) | \(21184262604460873/216872764416\) | \(384203331401573376\) | \([2, 2]\) | \(115200\) | \(2.1917\) | |
| 5082.v3 | 5082u4 | \([1, 1, 1, -174787, -547648639]\) | \(-333345918055753/72923718045024\) | \(-129188814863560762464\) | \([2]\) | \(230400\) | \(2.5383\) | |
| 5082.v4 | 5082u1 | \([1, 1, 1, -77987, 2740673]\) | \(29609739866953/15259926528\) | \(27033890699870208\) | \([4]\) | \(57600\) | \(1.8451\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5082.v have rank \(0\).
Complex multiplication
The elliptic curves in class 5082.v do not have complex multiplication.Modular form 5082.2.a.v
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 LMFDB 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 LMFDB labels.
