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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 98175t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 98175.bg3 | 98175t1 | \([1, 0, 1, -3345051, 2354506873]\) | \(264918160154242157473/536027170833\) | \(8375424544265625\) | \([2]\) | \(1474560\) | \(2.3063\) | \(\Gamma_0(N)\)-optimal |
| 98175.bg2 | 98175t2 | \([1, 0, 1, -3381176, 2301041873]\) | \(273594167224805799793/11903648120953281\) | \(185994501889895015625\) | \([2, 2]\) | \(2949120\) | \(2.6529\) | |
| 98175.bg4 | 98175t3 | \([1, 0, 1, 1720949, 8637881123]\) | \(36075142039228937567/2083708275110728497\) | \(-32557941798605132765625\) | \([2]\) | \(5898240\) | \(2.9994\) | |
| 98175.bg1 | 98175t4 | \([1, 0, 1, -9061301, -7457412877]\) | \(5265932508006615127873/1510137598013239041\) | \(23595899968956860015625\) | \([2]\) | \(5898240\) | \(2.9994\) |
Rank
sage: E.rank()
The elliptic curves in class 98175t have rank \(0\).
Complex multiplication
The elliptic curves in class 98175t do not have complex multiplication.Modular form 98175.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
