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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 9680.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9680.l1 | 9680ba1 | \([0, -1, 0, -9720, -371600]\) | \(-1693700041/32000\) | \(-1919025152000\) | \([]\) | \(13824\) | \(1.1515\) | \(\Gamma_0(N)\)-optimal |
9680.l2 | 9680ba2 | \([0, -1, 0, 38680, -1765520]\) | \(106718863559/83886080\) | \(-5030609294458880\) | \([]\) | \(41472\) | \(1.7008\) |
Rank
sage: E.rank()
The elliptic curves in class 9680.l have rank \(0\).
Complex multiplication
The elliptic curves in class 9680.l do not have complex multiplication.Modular form 9680.2.a.l
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.