# Properties

 Label 304920eu Number of curves $4$ Conductor $304920$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("eu1")

sage: E.isogeny_class()

## Elliptic curves in class 304920eu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
304920.eu4 304920eu1 $$[0, 0, 0, 396033, 91900226]$$ $$20777545136/23059575$$ $$-7623859837760812800$$ $$[2]$$ $$3932160$$ $$2.3097$$ $$\Gamma_0(N)$$-optimal
304920.eu3 304920eu2 $$[0, 0, 0, -2239347, 863012414]$$ $$939083699236/300155625$$ $$396944768412339840000$$ $$[2, 2]$$ $$7864320$$ $$2.6562$$
304920.eu1 304920eu3 $$[0, 0, 0, -32426427, 71060048246]$$ $$1425631925916578/270703125$$ $$715989842013600000000$$ $$[2]$$ $$15728640$$ $$3.0028$$
304920.eu2 304920eu4 $$[0, 0, 0, -14218347, -19982843386]$$ $$120186986927618/4332064275$$ $$11457991169662376908800$$ $$[2]$$ $$15728640$$ $$3.0028$$

## Rank

sage: E.rank()

The elliptic curves in class 304920eu have rank $$0$$.

## Complex multiplication

The elliptic curves in class 304920eu do not have complex multiplication.

## Modular form 304920.2.a.eu

sage: E.q_eigenform(10)

$$q + q^{5} + q^{7} + 2 q^{13} - 2 q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.