# Properties

 Label 344760.cn Number of curves $2$ Conductor $344760$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("cn1")

sage: E.isogeny_class()

## Elliptic curves in class 344760.cn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
344760.cn1 344760cn1 $$[0, 1, 0, -47491760, 125767815408]$$ $$2396726313900986596/4154072495625$$ $$20532136456740055680000$$ $$$$ $$30965760$$ $$3.1752$$ $$\Gamma_0(N)$$-optimal
344760.cn2 344760cn2 $$[0, 1, 0, -32640040, 205872052400]$$ $$-389032340685029858/1627263833203125$$ $$-16085999033301693600000000$$ $$$$ $$61931520$$ $$3.5218$$

## Rank

sage: E.rank()

The elliptic curves in class 344760.cn have rank $$1$$.

## Complex multiplication

The elliptic curves in class 344760.cn do not have complex multiplication.

## Modular form 344760.2.a.cn

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + q^{9} - 2 q^{11} + q^{15} - q^{17} + 8 q^{19} + O(q^{20})$$

## 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. 