Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 152460.bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152460.bw1 | 152460d2 | \([0, 0, 0, -1578174807, -24128278990706]\) | \(1314817350433665559504/190690249278375\) | \(63045209329573549278816000\) | \([2]\) | \(77414400\) | \(3.9654\) | |
| 152460.bw2 | 152460d1 | \([0, 0, 0, -89647932, -448495757831]\) | \(-3856034557002072064/1973796785296875\) | \(-40785525208417347492750000\) | \([2]\) | \(38707200\) | \(3.6189\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 152460.bw have rank \(0\).
Complex multiplication
The elliptic curves in class 152460.bw do not have complex multiplication.Modular form 152460.2.a.bw
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
