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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 15600.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15600.bj1 | 15600bx2 | \([0, -1, 0, -1345208, 601068912]\) | \(-168256703745625/30371328\) | \(-48594124800000000\) | \([]\) | \(233280\) | \(2.2056\) | |
| 15600.bj2 | 15600bx1 | \([0, -1, 0, 4792, 2748912]\) | \(7604375/2047032\) | \(-3275251200000000\) | \([]\) | \(77760\) | \(1.6563\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15600.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 15600.bj do not have complex multiplication.Modular form 15600.2.a.bj
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
