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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 350168i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 350168.i2 | 350168i1 | \([0, -1, 0, 2648, -2318148]\) | \(415292/469567\) | \(-2320906467023872\) | \([2]\) | \(1658880\) | \(1.6274\) | \(\Gamma_0(N)\)-optimal |
| 350168.i1 | 350168i2 | \([0, -1, 0, -247472, -46239220]\) | \(169556172914/4353013\) | \(43030860442658816\) | \([2]\) | \(3317760\) | \(1.9740\) |
Rank
sage: E.rank()
The elliptic curves in class 350168i have rank \(0\).
Complex multiplication
The elliptic curves in class 350168i do not have complex multiplication.Modular form 350168.2.a.i
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.
