# Properties

 Label 348480.gu Number of curves $4$ Conductor $348480$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("gu1")

sage: E.isogeny_class()

## Elliptic curves in class 348480.gu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
348480.gu1 348480gu4 $$[0, 0, 0, -1088984028, 13831853432848]$$ $$6749703004355978704/5671875$$ $$120013535423232000000$$ $$$$ $$53084160$$ $$3.5884$$
348480.gu2 348480gu3 $$[0, 0, 0, -68046528, 216222557848]$$ $$-26348629355659264/24169921875$$ $$-31963832232750000000000$$ $$$$ $$26542080$$ $$3.2418$$
348480.gu3 348480gu2 $$[0, 0, 0, -13748988, 18068527312]$$ $$13584145739344/1195803675$$ $$25302501678694171852800$$ $$$$ $$17694720$$ $$3.0391$$
348480.gu4 348480gu1 $$[0, 0, 0, 952512, 1314697912]$$ $$72268906496/606436875$$ $$-801990450465747840000$$ $$$$ $$8847360$$ $$2.6925$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 348480.gu have rank $$0$$.

## Complex multiplication

The elliptic curves in class 348480.gu do not have complex multiplication.

## Modular form 348480.2.a.gu

sage: E.q_eigenform(10)

$$q - q^{5} + 2q^{7} + 2q^{13} - 2q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 