# Properties

 Label 31200.q Number of curves $2$ Conductor $31200$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("q1")

sage: E.isogeny_class()

## Elliptic curves in class 31200.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
31200.q1 31200bf2 $$[0, -1, 0, -33008, -2296488]$$ $$497169541448/190125$$ $$1521000000000$$ $$[2]$$ $$92160$$ $$1.3034$$
31200.q2 31200bf1 $$[0, -1, 0, -1758, -46488]$$ $$-601211584/609375$$ $$-609375000000$$ $$[2]$$ $$46080$$ $$0.95688$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 31200.q have rank $$0$$.

## Complex multiplication

The elliptic curves in class 31200.q do not have complex multiplication.

## Modular form 31200.2.a.q

sage: E.q_eigenform(10)

$$q - q^{3} + 2q^{7} + q^{9} - 4q^{11} - q^{13} + 6q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.