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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 4275.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4275.a1 | 4275i2 | \([0, 0, 1, -987825, 377893156]\) | \(-9358714467168256/22284891\) | \(-253838836546875\) | \([]\) | \(67200\) | \(2.0054\) | |
4275.a2 | 4275i1 | \([0, 0, 1, 4425, 129406]\) | \(841232384/1121931\) | \(-12779495296875\) | \([]\) | \(13440\) | \(1.2007\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4275.a have rank \(0\).
Complex multiplication
The elliptic curves in class 4275.a do not have complex multiplication.Modular form 4275.2.a.a
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.