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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 7098.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7098.n1 | 7098i2 | \([1, 0, 1, -620989828, -5956328145220]\) | \(-5486773802537974663600129/2635437714\) | \(-12720754476874626\) | \([]\) | \(1382976\) | \(3.3290\) | |
7098.n2 | 7098i1 | \([1, 0, 1, 120662, -182269540]\) | \(40251338884511/2997011332224\) | \(-14466001271480793216\) | \([]\) | \(197568\) | \(2.3561\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7098.n have rank \(0\).
Complex multiplication
The elliptic curves in class 7098.n do not have complex multiplication.Modular form 7098.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.