Show commands:
SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 338800.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 338800.w1 | 338800w4 | \([0, 1, 0, -1264015408, -16807519120812]\) | \(1969902499564819009/63690429687500\) | \(7221214803687500000000000000\) | \([2]\) | \(238878720\) | \(4.1195\) | |
| 338800.w2 | 338800w2 | \([0, 1, 0, -173079408, 868584863188]\) | \(5057359576472449/51765560000\) | \(5869174223306240000000000\) | \([2]\) | \(79626240\) | \(3.5702\) | |
| 338800.w3 | 338800w1 | \([0, 1, 0, -2711408, 33440927188]\) | \(-19443408769/4249907200\) | \(-481854070344908800000000\) | \([2]\) | \(39813120\) | \(3.2236\) | \(\Gamma_0(N)\)-optimal |
| 338800.w4 | 338800w3 | \([0, 1, 0, 24392592, -900833952812]\) | \(14156681599871/3100231750000\) | \(-351503978192752000000000000\) | \([2]\) | \(119439360\) | \(3.7729\) |
Rank
sage: E.rank()
The elliptic curves in class 338800.w have rank \(1\).
Complex multiplication
The elliptic curves in class 338800.w do not have complex multiplication.Modular form 338800.2.a.w
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
