# Properties

 Label 51480bu Number of curves $4$ Conductor $51480$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bu1")

sage: E.isogeny_class()

## Elliptic curves in class 51480bu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51480.bb4 51480bu1 $$[0, 0, 0, -822207, -390626494]$$ $$-329381898333928144/162600887109375$$ $$-30345227955900000000$$ $$[4]$$ $$1376256$$ $$2.4435$$ $$\Gamma_0(N)$$-optimal
51480.bb3 51480bu2 $$[0, 0, 0, -14434707, -21106128994]$$ $$445574312599094932036/61129333175625$$ $$45632802698271360000$$ $$[2, 2]$$ $$2752512$$ $$2.7901$$
51480.bb2 51480bu3 $$[0, 0, 0, -15721707, -17118745594]$$ $$287849398425814280018/81784533026485575$$ $$122103653532278751590400$$ $$[2]$$ $$5505024$$ $$3.1367$$
51480.bb1 51480bu4 $$[0, 0, 0, -230947707, -1350885672394]$$ $$912446049969377120252018/17177299425$$ $$25645570623129600$$ $$[2]$$ $$5505024$$ $$3.1367$$

## Rank

sage: E.rank()

The elliptic curves in class 51480bu have rank $$0$$.

## Complex multiplication

The elliptic curves in class 51480bu do not have complex multiplication.

## Modular form 51480.2.a.bu

sage: E.q_eigenform(10)

$$q + q^{5} - 4 q^{7} + q^{11} + q^{13} + 2 q^{17} + 4 q^{19} + O(q^{20})$$

## 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 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.