Show commands:
SageMath
E = EllipticCurve("ew1")
E.isogeny_class()
Elliptic curves in class 44352.ew
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 44352.ew1 | 44352n1 | \([0, 0, 0, -276, 1832]\) | \(-84098304/3773\) | \(-104315904\) | \([]\) | \(18432\) | \(0.30308\) | \(\Gamma_0(N)\)-optimal |
| 44352.ew2 | 44352n2 | \([0, 0, 0, 1404, 4968]\) | \(15185664/9317\) | \(-187787787264\) | \([]\) | \(55296\) | \(0.85238\) |
Rank
sage: E.rank()
The elliptic curves in class 44352.ew have rank \(1\).
Complex multiplication
The elliptic curves in class 44352.ew do not have complex multiplication.Modular form 44352.2.a.ew
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.
