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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 9680.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9680.f1 | 9680q2 | \([0, -1, 0, -436, -3364]\) | \(-296587984/125\) | \(-3872000\) | \([]\) | \(1728\) | \(0.22525\) | |
9680.f2 | 9680q1 | \([0, -1, 0, 4, -20]\) | \(176/5\) | \(-154880\) | \([]\) | \(576\) | \(-0.32406\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9680.f have rank \(1\).
Complex multiplication
The elliptic curves in class 9680.f do not have complex multiplication.Modular form 9680.2.a.f
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.