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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 14784.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14784.g1 | 14784o4 | \([0, -1, 0, -4289, 109473]\) | \(266344154504/237699\) | \(7788920832\) | \([4]\) | \(16384\) | \(0.82281\) | |
14784.g2 | 14784o3 | \([0, -1, 0, -2849, -56991]\) | \(78073482824/922383\) | \(30224646144\) | \([2]\) | \(16384\) | \(0.82281\) | |
14784.g3 | 14784o2 | \([0, -1, 0, -329, 969]\) | \(964430272/480249\) | \(1967099904\) | \([2, 2]\) | \(8192\) | \(0.47623\) | |
14784.g4 | 14784o1 | \([0, -1, 0, 76, 78]\) | \(748613312/505197\) | \(-32332608\) | \([2]\) | \(4096\) | \(0.12966\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 14784.g have rank \(2\).
Complex multiplication
The elliptic curves in class 14784.g do not have complex multiplication.Modular form 14784.2.a.g
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.