# Properties

 Label 348480cp Number of curves $4$ Conductor $348480$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cp1")

sage: E.isogeny_class()

## Elliptic curves in class 348480cp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
348480.cp4 348480cp1 $$[0, 0, 0, 952512, -1314697912]$$ $$72268906496/606436875$$ $$-801990450465747840000$$ $$[2]$$ $$8847360$$ $$2.6925$$ $$\Gamma_0(N)$$-optimal
348480.cp3 348480cp2 $$[0, 0, 0, -13748988, -18068527312]$$ $$13584145739344/1195803675$$ $$25302501678694171852800$$ $$[2]$$ $$17694720$$ $$3.0391$$
348480.cp2 348480cp3 $$[0, 0, 0, -68046528, -216222557848]$$ $$-26348629355659264/24169921875$$ $$-31963832232750000000000$$ $$[2]$$ $$26542080$$ $$3.2418$$
348480.cp1 348480cp4 $$[0, 0, 0, -1088984028, -13831853432848]$$ $$6749703004355978704/5671875$$ $$120013535423232000000$$ $$[2]$$ $$53084160$$ $$3.5884$$

## Rank

sage: E.rank()

The elliptic curves in class 348480cp have rank $$1$$.

## Complex multiplication

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

## Modular form 348480.2.a.cp

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 Cremona 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 Cremona labels.