Properties

 Label 2200.g Number of curves $2$ Conductor $2200$ CM no Rank $0$ Graph

Related objects

Show commands: SageMath
E = EllipticCurve("g1")

E.isogeny_class()

Elliptic curves in class 2200.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2200.g1 2200a2 $$[0, 0, 0, -575, -4750]$$ $$5256144/605$$ $$2420000000$$ $$[2]$$ $$768$$ $$0.53265$$
2200.g2 2200a1 $$[0, 0, 0, 50, -375]$$ $$55296/275$$ $$-68750000$$ $$[2]$$ $$384$$ $$0.18608$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 2200.g have rank $$0$$.

Complex multiplication

The elliptic curves in class 2200.g do not have complex multiplication.

Modular form2200.2.a.g

sage: E.q_eigenform(10)

$$q + 2 q^{7} - 3 q^{9} + q^{11} + 4 q^{13} + 4 q^{17} + O(q^{20})$$

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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.