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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 103455.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
103455.n1 | 103455bf2 | \([1, -1, 1, -33782, 2257544]\) | \(3301293169/218405\) | \(282063061769445\) | \([2]\) | \(368640\) | \(1.5222\) | |
103455.n2 | 103455bf1 | \([1, -1, 1, -6557, -160036]\) | \(24137569/5225\) | \(6747920138025\) | \([2]\) | \(184320\) | \(1.1756\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 103455.n have rank \(1\).
Complex multiplication
The elliptic curves in class 103455.n do not have complex multiplication.Modular form 103455.2.a.n
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.