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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 3600.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3600.j1 | 3600bj2 | \([0, 0, 0, -30000, -2050000]\) | \(-102400/3\) | \(-87480000000000\) | \([]\) | \(9600\) | \(1.4541\) | |
| 3600.j2 | 3600bj1 | \([0, 0, 0, 240, 6320]\) | \(20480/243\) | \(-18139852800\) | \([]\) | \(1920\) | \(0.64935\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3600.j have rank \(1\).
Complex multiplication
The elliptic curves in class 3600.j do not have complex multiplication.Modular form 3600.2.a.j
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.
