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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 285770.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
285770.t1 | 285770t2 | \([1, 1, 1, -11163556, -14824153947]\) | \(-32391289681150609/1228250000000\) | \(-5834315534008250000000\) | \([]\) | \(17418240\) | \(2.9466\) | |
285770.t2 | 285770t1 | \([1, 1, 1, 670684, -65350491]\) | \(7023836099951/4456448000\) | \(-21168592544595968000\) | \([]\) | \(5806080\) | \(2.3973\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 285770.t have rank \(1\).
Complex multiplication
The elliptic curves in class 285770.t do not have complex multiplication.Modular form 285770.2.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.