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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 92169.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92169.t1 | 92169k2 | \([0, 0, 1, -13257930, -18580683956]\) | \(-3004935183806464000/2037123\) | \(-174716137709883\) | \([]\) | \(1555200\) | \(2.4824\) | |
| 92169.t2 | 92169k1 | \([0, 0, 1, -160230, -26613113]\) | \(-5304438784000/497763387\) | \(-42691234878811827\) | \([]\) | \(518400\) | \(1.9331\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 92169.t have rank \(1\).
Complex multiplication
The elliptic curves in class 92169.t do not have complex multiplication.Modular form 92169.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
