Show commands:
SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 55473.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
55473.n1 | 55473l4 | \([1, 0, 1, -246302, 46982081]\) | \(347873904937/395307\) | \(1877749457196987\) | \([2]\) | \(422400\) | \(1.8442\) | |
55473.n2 | 55473l2 | \([1, 0, 1, -19367, 324245]\) | \(169112377/88209\) | \(419001944994369\) | \([2, 2]\) | \(211200\) | \(1.4976\) | |
55473.n3 | 55473l1 | \([1, 0, 1, -10962, -438929]\) | \(30664297/297\) | \(1410780959577\) | \([2]\) | \(105600\) | \(1.1510\) | \(\Gamma_0(N)\)-optimal |
55473.n4 | 55473l3 | \([1, 0, 1, 73088, 2543165]\) | \(9090072503/5845851\) | \(-27768401627354091\) | \([2]\) | \(422400\) | \(1.8442\) |
Rank
sage: E.rank()
The elliptic curves in class 55473.n have rank \(0\).
Complex multiplication
The elliptic curves in class 55473.n do not have complex multiplication.Modular form 55473.2.a.n
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.