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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 129360.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
129360.f1 | 129360q1 | \([0, -1, 0, -4916, -74304]\) | \(1272112/495\) | \(5113609079040\) | \([2]\) | \(286720\) | \(1.1374\) | \(\Gamma_0(N)\)-optimal |
129360.f2 | 129360q2 | \([0, -1, 0, 15664, -551760]\) | \(10285412/9075\) | \(-374997999129600\) | \([2]\) | \(573440\) | \(1.4840\) |
Rank
sage: E.rank()
The elliptic curves in class 129360.f have rank \(0\).
Complex multiplication
The elliptic curves in class 129360.f do not have complex multiplication.Modular form 129360.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.