# Properties

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

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("ci1")

sage: E.isogeny_class()

## Elliptic curves in class 31200.ci

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
31200.ci1 31200cd1 $$[0, 1, 0, -358, -2212]$$ $$5088448/1053$$ $$1053000000$$ $$[2]$$ $$16384$$ $$0.44642$$ $$\Gamma_0(N)$$-optimal
31200.ci2 31200cd2 $$[0, 1, 0, 767, -12337]$$ $$778688/1521$$ $$-97344000000$$ $$[2]$$ $$32768$$ $$0.79299$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 31200.2.a.ci

sage: E.q_eigenform(10)

$$q + q^{3} + 2 q^{7} + q^{9} + 6 q^{11} + q^{13} + 2 q^{17} + 6 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.