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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 195195n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 195195.f3 | 195195n1 | \([1, 1, 1, -34395, 2439120]\) | \(932288503609/779625\) | \(3763100966625\) | \([2]\) | \(663552\) | \(1.3409\) | \(\Gamma_0(N)\)-optimal |
| 195195.f2 | 195195n2 | \([1, 1, 1, -42000, 1270992]\) | \(1697509118089/833765625\) | \(4024427422640625\) | \([2, 2]\) | \(1327104\) | \(1.6875\) | |
| 195195.f4 | 195195n3 | \([1, 1, 1, 153195, 9937650]\) | \(82375335041831/56396484375\) | \(-272215058349609375\) | \([2]\) | \(2654208\) | \(2.0341\) | |
| 195195.f1 | 195195n4 | \([1, 1, 1, -358875, -82003758]\) | \(1058993490188089/13182390375\) | \(63628880503563375\) | \([2]\) | \(2654208\) | \(2.0341\) |
Rank
sage: E.rank()
The elliptic curves in class 195195n have rank \(1\).
Complex multiplication
The elliptic curves in class 195195n do not have complex multiplication.Modular form 195195.2.a.n
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
