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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 37830.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37830.x1 | 37830v4 | \([1, 0, 0, -445019426, -3613339910844]\) | \(9746767800165691625640374914849/317066485593528403200000\) | \(317066485593528403200000\) | \([2]\) | \(12390400\) | \(3.6036\) | |
| 37830.x2 | 37830v2 | \([1, 0, 0, -29019426, -51298310844]\) | \(2702652238257846790070914849/427326827765760000000000\) | \(427326827765760000000000\) | \([2, 2]\) | \(6195200\) | \(3.2570\) | |
| 37830.x3 | 37830v1 | \([1, 0, 0, -8047906, 8013342020]\) | \(57646427881253842993467169/5615260858633420800000\) | \(5615260858633420800000\) | \([2]\) | \(3097600\) | \(2.9105\) | \(\Gamma_0(N)\)-optimal |
| 37830.x4 | 37830v3 | \([1, 0, 0, 51436254, -285118608060]\) | \(15049833955501140831007387871/43828862695312500000000000\) | \(-43828862695312500000000000\) | \([2]\) | \(12390400\) | \(3.6036\) |
Rank
sage: E.rank()
The elliptic curves in class 37830.x have rank \(0\).
Complex multiplication
The elliptic curves in class 37830.x do not have complex multiplication.Modular form 37830.2.a.x
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.
