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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 271062t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 271062.t3 | 271062t1 | \([1, -1, 1, -107816, 13685595]\) | \(-3753503985421/10392624\) | \(-383758418351088\) | \([2]\) | \(1843200\) | \(1.6714\) | \(\Gamma_0(N)\)-optimal |
| 271062.t2 | 271062t2 | \([1, -1, 1, -1726196, 873369051]\) | \(15404978391891661/117612\) | \(4342945063644\) | \([2]\) | \(3686400\) | \(2.0180\) | |
| 271062.t4 | 271062t3 | \([1, -1, 1, 776299, -246376083]\) | \(1401130594505699/1519867920384\) | \(-56122699063212638208\) | \([2]\) | \(9216000\) | \(2.4761\) | |
| 271062.t1 | 271062t4 | \([1, -1, 1, -4338581, -2298465939]\) | \(244587381607181341/79679768374272\) | \(2942258075139797720064\) | \([2]\) | \(18432000\) | \(2.8227\) |
Rank
sage: E.rank()
The elliptic curves in class 271062t have rank \(1\).
Complex multiplication
The elliptic curves in class 271062t do not have complex multiplication.Modular form 271062.2.a.t
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
