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SageMath
E = EllipticCurve("eb1")
E.isogeny_class()
Elliptic curves in class 39600eb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
39600.er2 | 39600eb1 | \([0, 0, 0, 35925, -10579750]\) | \(109902239/1100000\) | \(-51321600000000000\) | \([]\) | \(345600\) | \(1.8875\) | \(\Gamma_0(N)\)-optimal |
39600.er1 | 39600eb2 | \([0, 0, 0, -21384075, -38061319750]\) | \(-23178622194826561/1610510\) | \(-75139954560000000\) | \([]\) | \(1728000\) | \(2.6922\) |
Rank
sage: E.rank()
The elliptic curves in class 39600eb have rank \(0\).
Complex multiplication
The elliptic curves in class 39600eb do not have complex multiplication.Modular form 39600.2.a.eb
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.