Show commands:
SageMath
E = EllipticCurve("hi1")
E.isogeny_class()
Elliptic curves in class 78400.hi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
78400.hi1 | 78400kj2 | \([0, 1, 0, -29073, 1907933]\) | \(-2887553024/16807\) | \(-15818613944000\) | \([]\) | \(153600\) | \(1.3737\) | |
78400.hi2 | 78400kj1 | \([0, 1, 0, 327, -3067]\) | \(4096/7\) | \(-6588344000\) | \([]\) | \(30720\) | \(0.56900\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 78400.hi have rank \(0\).
Complex multiplication
The elliptic curves in class 78400.hi do not have complex multiplication.Modular form 78400.2.a.hi
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.