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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 7840.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7840.l1 | 7840q3 | \([0, 0, 0, -640283, 197199618]\) | \(481927184300808/1225\) | \(73789452800\) | \([2]\) | \(36864\) | \(1.7490\) | |
| 7840.l2 | 7840q2 | \([0, 0, 0, -52283, 1037918]\) | \(262389836808/144120025\) | \(8681255332467200\) | \([2]\) | \(36864\) | \(1.7490\) | |
| 7840.l3 | 7840q1 | \([0, 0, 0, -40033, 3078768]\) | \(942344950464/1500625\) | \(11299009960000\) | \([2, 2]\) | \(18432\) | \(1.4024\) | \(\Gamma_0(N)\)-optimal |
| 7840.l4 | 7840q4 | \([0, 0, 0, -28028, 4961152]\) | \(-5053029696/19140625\) | \(-9223681600000000\) | \([2]\) | \(36864\) | \(1.7490\) |
Rank
sage: E.rank()
The elliptic curves in class 7840.l have rank \(1\).
Complex multiplication
The elliptic curves in class 7840.l do not have complex multiplication.Modular form 7840.2.a.l
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.
