Show commands:
SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 15300bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15300.l2 | 15300bg1 | \([0, 0, 0, 2625, 13750]\) | \(27440/17\) | \(-1239300000000\) | \([]\) | \(10800\) | \(1.0096\) | \(\Gamma_0(N)\)-optimal |
| 15300.l1 | 15300bg2 | \([0, 0, 0, -42375, 3478750]\) | \(-115431760/4913\) | \(-358157700000000\) | \([3]\) | \(32400\) | \(1.5589\) |
Rank
sage: E.rank()
The elliptic curves in class 15300bg have rank \(1\).
Complex multiplication
The elliptic curves in class 15300bg do not have complex multiplication.Modular form 15300.2.a.bg
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
