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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 13860.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13860.n1 | 13860d1 | \([0, 0, 0, -48, 117]\) | \(28311552/2695\) | \(1164240\) | \([2]\) | \(2688\) | \(-0.098164\) | \(\Gamma_0(N)\)-optimal |
13860.n2 | 13860d2 | \([0, 0, 0, 57, 558]\) | \(2963088/21175\) | \(-146361600\) | \([2]\) | \(5376\) | \(0.24841\) |
Rank
sage: E.rank()
The elliptic curves in class 13860.n have rank \(0\).
Complex multiplication
The elliptic curves in class 13860.n do not have complex multiplication.Modular form 13860.2.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.