Properties

 Label 56550.cg Number of curves $4$ Conductor $56550$ CM no Rank $0$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("cg1")

sage: E.isogeny_class()

Elliptic curves in class 56550.cg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
56550.cg1 56550bv4 $$[1, 0, 0, -208813, -33642883]$$ $$64443098670429961/6032611833300$$ $$94259559895312500$$ $$$$ $$1179648$$ $$1.9955$$
56550.cg2 56550bv2 $$[1, 0, 0, -46313, 3244617]$$ $$703093388853961/115124490000$$ $$1798820156250000$$ $$[2, 2]$$ $$589824$$ $$1.6489$$
56550.cg3 56550bv1 $$[1, 0, 0, -44313, 3586617]$$ $$615882348586441/21715200$$ $$339300000000$$ $$$$ $$294912$$ $$1.3023$$ $$\Gamma_0(N)$$-optimal
56550.cg4 56550bv3 $$[1, 0, 0, 84187, 18252117]$$ $$4223169036960119/11647532812500$$ $$-181992700195312500$$ $$$$ $$1179648$$ $$1.9955$$

Rank

sage: E.rank()

The elliptic curves in class 56550.cg have rank $$0$$.

Complex multiplication

The elliptic curves in class 56550.cg do not have complex multiplication.

Modular form 56550.2.a.cg

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} + 4 q^{7} + q^{8} + q^{9} - 4 q^{11} + q^{12} - q^{13} + 4 q^{14} + q^{16} + 6 q^{17} + q^{18} - 4 q^{19} + O(q^{20})$$ 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. 