Show commands:
SageMath
E = EllipticCurve("ew1")
E.isogeny_class()
Elliptic curves in class 35280.ew
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35280.ew1 | 35280di2 | \([0, 0, 0, -28707, -1872094]\) | \(68971442301/400\) | \(15173222400\) | \([2]\) | \(49152\) | \(1.1438\) | |
35280.ew2 | 35280di1 | \([0, 0, 0, -1827, -28126]\) | \(17779581/1280\) | \(48554311680\) | \([2]\) | \(24576\) | \(0.79720\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 35280.ew have rank \(0\).
Complex multiplication
The elliptic curves in class 35280.ew do not have complex multiplication.Modular form 35280.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.