# Properties

 Label 355740du Number of curves $2$ Conductor $355740$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("du1")

sage: E.isogeny_class()

## Elliptic curves in class 355740du

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
355740.du2 355740du1 $$[0, 1, 0, -126485, 54251448]$$ $$-67108864/343035$$ $$-1143938738461281840$$ $$$$ $$5529600$$ $$2.1494$$ $$\Gamma_0(N)$$-optimal
355740.du1 355740du2 $$[0, 1, 0, -3061340, 2056996500]$$ $$59466754384/121275$$ $$6470764581195129600$$ $$$$ $$11059200$$ $$2.4960$$

## Rank

sage: E.rank()

The elliptic curves in class 355740du have rank $$0$$.

## Complex multiplication

The elliptic curves in class 355740du do not have complex multiplication.

## Modular form 355740.2.a.du

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + q^{9} - 6q^{13} + q^{15} + 2q^{17} + O(q^{20})$$ ## 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 Cremona 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 Cremona labels. 