# Properties

 Label 344760.cl Number of curves $4$ Conductor $344760$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("cl1")

sage: E.isogeny_class()

## Elliptic curves in class 344760.cl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
344760.cl1 344760cl4 $$[0, 1, 0, -5525680, -5001293920]$$ $$1887517194957938/21849165$$ $$215985656349665280$$ $$[2]$$ $$8257536$$ $$2.4773$$
344760.cl2 344760cl2 $$[0, 1, 0, -354280, -73984000]$$ $$994958062276/98903025$$ $$488843275465958400$$ $$[2, 2]$$ $$4128768$$ $$2.1308$$
344760.cl3 344760cl1 $$[0, 1, 0, -80500, 7492928]$$ $$46689225424/7249905$$ $$8958440116005120$$ $$[4]$$ $$2064384$$ $$1.7842$$ $$\Gamma_0(N)$$-optimal
344760.cl4 344760cl3 $$[0, 1, 0, 436640, -356816992]$$ $$931329171502/6107473125$$ $$-60374233593872640000$$ $$[2]$$ $$8257536$$ $$2.4773$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 344760.2.a.cl

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + q^{9} - 4 q^{11} + q^{15} + q^{17} - 8 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.