# Properties

 Label 379050bb Number of curves $2$ Conductor $379050$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bb1")

sage: E.isogeny_class()

## Elliptic curves in class 379050bb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
379050.bb1 379050bb1 $$[1, 1, 0, -410825, 58220625]$$ $$1520875/588$$ $$2964693223344562500$$ $$[2]$$ $$8755200$$ $$2.2434$$ $$\Gamma_0(N)$$-optimal
379050.bb2 379050bb2 $$[1, 1, 0, 1303925, 420032875]$$ $$48627125/43218$$ $$-217904951915825343750$$ $$[2]$$ $$17510400$$ $$2.5900$$

## Rank

sage: E.rank()

The elliptic curves in class 379050bb have rank $$0$$.

## Complex multiplication

The elliptic curves in class 379050bb do not have complex multiplication.

## Modular form 379050.2.a.bb

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{6} + q^{7} - q^{8} + q^{9} - 6q^{11} - q^{12} - 2q^{13} - q^{14} + q^{16} - 2q^{17} - q^{18} + O(q^{20})$$

## 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.