# Properties

 Label 31200.cf Number of curves $2$ Conductor $31200$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("cf1")

sage: E.isogeny_class()

## Elliptic curves in class 31200.cf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
31200.cf1 31200o2 $$[0, 1, 0, -833, -3537]$$ $$1000000/507$$ $$32448000000$$ $$$$ $$18432$$ $$0.70940$$
31200.cf2 31200o1 $$[0, 1, 0, -458, 3588]$$ $$10648000/117$$ $$117000000$$ $$$$ $$9216$$ $$0.36283$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 31200.2.a.cf

sage: E.q_eigenform(10)

$$q + q^{3} + 2q^{7} + q^{9} - q^{13} - 2q^{17} + 2q^{19} + O(q^{20})$$ ## 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. 