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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 53040.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 53040.l1 | 53040g4 | \([0, -1, 0, -62496, 6034320]\) | \(26362547147244676/244298925\) | \(250162099200\) | \([4]\) | \(147456\) | \(1.3508\) | |
| 53040.l2 | 53040g2 | \([0, -1, 0, -3996, 90720]\) | \(27572037674704/2472575625\) | \(632979360000\) | \([2, 2]\) | \(73728\) | \(1.0042\) | |
| 53040.l3 | 53040g1 | \([0, -1, 0, -871, -8030]\) | \(4572531595264/776953125\) | \(12431250000\) | \([2]\) | \(36864\) | \(0.65763\) | \(\Gamma_0(N)\)-optimal |
| 53040.l4 | 53040g3 | \([0, -1, 0, 4504, 417120]\) | \(9865576607324/79640206425\) | \(-81551571379200\) | \([2]\) | \(147456\) | \(1.3508\) |
Rank
sage: E.rank()
The elliptic curves in class 53040.l have rank \(1\).
Complex multiplication
The elliptic curves in class 53040.l do not have complex multiplication.Modular form 53040.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
