Show commands:
SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 23104.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23104.bj1 | 23104l3 | \([0, 1, 0, -1975873, 8598438175]\) | \(-69173457625/2550136832\) | \(-31450315864667322318848\) | \([]\) | \(1244160\) | \(2.9971\) | |
| 23104.bj2 | 23104l1 | \([0, 1, 0, -358593, -82797409]\) | \(-413493625/152\) | \(-1874584905187328\) | \([]\) | \(138240\) | \(1.8985\) | \(\Gamma_0(N)\)-optimal |
| 23104.bj3 | 23104l2 | \([0, 1, 0, 219007, -314091553]\) | \(94196375/3511808\) | \(-43310409649448026112\) | \([]\) | \(414720\) | \(2.4478\) |
Rank
sage: E.rank()
The elliptic curves in class 23104.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 23104.bj do not have complex multiplication.Modular form 23104.2.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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
