Show commands:
SageMath
E = EllipticCurve("dt1")
E.isogeny_class()
Elliptic curves in class 179520.dt
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
179520.dt1 | 179520dc2 | \([0, -1, 0, -46022945, 119735819457]\) | \(41125104693338423360329/179205840000000000\) | \(46977735720960000000000\) | \([2]\) | \(19169280\) | \(3.2033\) | |
179520.dt2 | 179520dc1 | \([0, -1, 0, -1458465, 3716652225]\) | \(-1308796492121439049/22000592486400000\) | \(-5767323316754841600000\) | \([2]\) | \(9584640\) | \(2.8568\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 179520.dt have rank \(0\).
Complex multiplication
The elliptic curves in class 179520.dt do not have complex multiplication.Modular form 179520.2.a.dt
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.