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SageMath
E = EllipticCurve("ef1")
E.isogeny_class()
Elliptic curves in class 39600ef
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
39600.ff1 | 39600ef1 | \([0, 0, 0, -318675, 69903250]\) | \(-76711450249/851840\) | \(-39743447040000000\) | \([]\) | \(483840\) | \(2.0000\) | \(\Gamma_0(N)\)-optimal |
39600.ff2 | 39600ef2 | \([0, 0, 0, 1067325, 362349250]\) | \(2882081488391/2883584000\) | \(-134536495104000000000\) | \([]\) | \(1451520\) | \(2.5493\) |
Rank
sage: E.rank()
The elliptic curves in class 39600ef have rank \(0\).
Complex multiplication
The elliptic curves in class 39600ef do not have complex multiplication.Modular form 39600.2.a.ef
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 Cremona 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 Cremona labels.