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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 116688l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116688.n1 | 116688l1 | \([0, -1, 0, -1496, 16368]\) | \(90458382169/25788048\) | \(105627844608\) | \([2]\) | \(153600\) | \(0.82190\) | \(\Gamma_0(N)\)-optimal |
| 116688.n2 | 116688l2 | \([0, -1, 0, 3944, 103408]\) | \(1656015369191/2114999172\) | \(-8663036608512\) | \([2]\) | \(307200\) | \(1.1685\) |
Rank
sage: E.rank()
The elliptic curves in class 116688l have rank \(1\).
Complex multiplication
The elliptic curves in class 116688l do not have complex multiplication.Modular form 116688.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
