Show commands:
SageMath
E = EllipticCurve("es1")
E.isogeny_class()
Elliptic curves in class 14400.es
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14400.es1 | 14400dj2 | \([0, 0, 0, -11340, 464400]\) | \(1000188\) | \(161243136000\) | \([2]\) | \(24576\) | \(1.0699\) | |
14400.es2 | 14400dj1 | \([0, 0, 0, -540, 10800]\) | \(-432\) | \(-40310784000\) | \([2]\) | \(12288\) | \(0.72338\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 14400.es have rank \(1\).
Complex multiplication
The elliptic curves in class 14400.es do not have complex multiplication.Modular form 14400.2.a.es
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.