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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 116886.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
116886.t1 | 116886o2 | \([1, 0, 1, -16046066, 24738734612]\) | \(3776104682692733708238625/3408048\) | \(412373808\) | \([]\) | \(2488320\) | \(2.3332\) | |
116886.t2 | 116886o1 | \([1, 0, 1, -198146, 33903956]\) | \(7110352307247726625/6866458324992\) | \(830841457324032\) | \([]\) | \(829440\) | \(1.7839\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 116886.t have rank \(2\).
Complex multiplication
The elliptic curves in class 116886.t do not have complex multiplication.Modular form 116886.2.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.