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SageMath
E = EllipticCurve("ey1")
E.isogeny_class()
Elliptic curves in class 39600ey
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 39600.bp2 | 39600ey1 | \([0, 0, 0, 17925, -3416150]\) | \(341297975/2898918\) | \(-5410076728320000\) | \([]\) | \(230400\) | \(1.7003\) | \(\Gamma_0(N)\)-optimal |
| 39600.bp1 | 39600ey2 | \([0, 0, 0, -2080875, 1179396250]\) | \(-854307420745/20785248\) | \(-24243913267200000000\) | \([]\) | \(1152000\) | \(2.5050\) |
Rank
sage: E.rank()
The elliptic curves in class 39600ey have rank \(1\).
Complex multiplication
The elliptic curves in class 39600ey do not have complex multiplication.Modular form 39600.2.a.ey
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.
