Show commands:
SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 38808.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38808.p1 | 38808cn4 | \([0, 0, 0, -310611, 66630494]\) | \(37736227588/33\) | \(2898208760832\) | \([2]\) | \(221184\) | \(1.6916\) | |
| 38808.p2 | 38808cn3 | \([0, 0, 0, -46011, -2345434]\) | \(122657188/43923\) | \(3857515860667392\) | \([2]\) | \(221184\) | \(1.6916\) | |
| 38808.p3 | 38808cn2 | \([0, 0, 0, -19551, 1025570]\) | \(37642192/1089\) | \(23910222276864\) | \([2, 2]\) | \(110592\) | \(1.3450\) | |
| 38808.p4 | 38808cn1 | \([0, 0, 0, 294, 53165]\) | \(2048/891\) | \(-1222681820976\) | \([2]\) | \(55296\) | \(0.99844\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 38808.p have rank \(1\).
Complex multiplication
The elliptic curves in class 38808.p do not have complex multiplication.Modular form 38808.2.a.p
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
