Show commands:
SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 9438.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9438.t1 | 9438u3 | \([1, 1, 1, -2509482, -1531161081]\) | \(986551739719628473/111045168\) | \(196723288867248\) | \([2]\) | \(204800\) | \(2.1670\) | |
| 9438.t2 | 9438u4 | \([1, 1, 1, -283082, 19543943]\) | \(1416134368422073/725251155408\) | \(1284826662125751888\) | \([2]\) | \(204800\) | \(2.1670\) | |
| 9438.t3 | 9438u2 | \([1, 1, 1, -157242, -23845689]\) | \(242702053576633/2554695936\) | \(4525799687076096\) | \([2, 2]\) | \(102400\) | \(1.8205\) | |
| 9438.t4 | 9438u1 | \([1, 1, 1, -2362, -923449]\) | \(-822656953/207028224\) | \(-366763127537664\) | \([2]\) | \(51200\) | \(1.4739\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9438.t have rank \(1\).
Complex multiplication
The elliptic curves in class 9438.t do not have complex multiplication.Modular form 9438.2.a.t
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.
