Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 1344.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1344.k1 | 1344i2 | \([0, 1, 0, -145, -721]\) | \(20720464/63\) | \(1032192\) | \([2]\) | \(384\) | \(0.022587\) | |
1344.k2 | 1344i1 | \([0, 1, 0, -5, -21]\) | \(-16384/147\) | \(-150528\) | \([2]\) | \(192\) | \(-0.32399\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1344.k have rank \(0\).
Complex multiplication
The elliptic curves in class 1344.k do not have complex multiplication.Modular form 1344.2.a.k
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.