# Properties

 Label 379050.p Number of curves $2$ Conductor $379050$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("p1")

sage: E.isogeny_class()

## Elliptic curves in class 379050.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
379050.p1 379050p1 $$[1, 1, 0, -11788500, 14202450000]$$ $$1690513270434786979/164670952320000$$ $$17648094718170000000000$$ $$$$ $$38707200$$ $$3.0059$$ $$\Gamma_0(N)$$-optimal
379050.p2 379050p2 $$[1, 1, 0, 14279500, 68241414000]$$ $$3004566620369762141/20506979587500000$$ $$-2197771452979101562500000$$ $$$$ $$77414400$$ $$3.3525$$

## Rank

sage: E.rank()

The elliptic curves in class 379050.p have rank $$1$$.

## Complex multiplication

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

## Modular form 379050.2.a.p

sage: E.q_eigenform(10)

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