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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 19074t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19074.w1 | 19074t1 | \([1, 1, 1, -261262, 50884811]\) | \(81706955619457/744505344\) | \(17970549111668736\) | \([2]\) | \(322560\) | \(1.9412\) | \(\Gamma_0(N)\)-optimal |
19074.w2 | 19074t2 | \([1, 1, 1, -76302, 121761483]\) | \(-2035346265217/264305213568\) | \(-6379685329557336192\) | \([2]\) | \(645120\) | \(2.2877\) |
Rank
sage: E.rank()
The elliptic curves in class 19074t have rank \(1\).
Complex multiplication
The elliptic curves in class 19074t do not have complex multiplication.Modular form 19074.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.