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SageMath
E = EllipticCurve("jn1")
E.isogeny_class()
Elliptic curves in class 110400.jn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
110400.jn1 | 110400id2 | \([0, 1, 0, -388033, 92864063]\) | \(1577505447721/838350\) | \(3433881600000000\) | \([2]\) | \(1327104\) | \(1.9308\) | |
110400.jn2 | 110400id1 | \([0, 1, 0, -20033, 1968063]\) | \(-217081801/285660\) | \(-1170063360000000\) | \([2]\) | \(663552\) | \(1.5842\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 110400.jn have rank \(1\).
Complex multiplication
The elliptic curves in class 110400.jn do not have complex multiplication.Modular form 110400.2.a.jn
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.