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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 162240.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162240.l1 | 162240ht4 | \([0, -1, 0, -12936161, -16992756639]\) | \(189208196468929/10860320250\) | \(13741769759282233344000\) | \([2]\) | \(9289728\) | \(3.0020\) | |
| 162240.l2 | 162240ht2 | \([0, -1, 0, -2228321, 1275402465]\) | \(967068262369/4928040\) | \(6235542735909027840\) | \([2]\) | \(3096576\) | \(2.4527\) | |
| 162240.l3 | 162240ht1 | \([0, -1, 0, -65121, 41080545]\) | \(-24137569/561600\) | \(-710603160787353600\) | \([2]\) | \(1548288\) | \(2.1061\) | \(\Gamma_0(N)\)-optimal |
| 162240.l4 | 162240ht3 | \([0, -1, 0, 583839, -1085124639]\) | \(17394111071/411937500\) | \(-521232353181696000000\) | \([2]\) | \(4644864\) | \(2.6554\) |
Rank
sage: E.rank()
The elliptic curves in class 162240.l have rank \(1\).
Complex multiplication
The elliptic curves in class 162240.l do not have complex multiplication.Modular form 162240.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
