# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 379050i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
379050.i2 379050i1 $$[1, 1, 0, -631781775, -6039445606875]$$ $$105093573726037969/1444738498560$$ $$383387615125835120640000000$$ $$[]$$ $$248209920$$ $$3.9068$$ $$\Gamma_0(N)$$-optimal
379050.i1 379050i2 $$[1, 1, 0, -51004277775, -4433636652694875]$$ $$55296123367985268658129/148176000$$ $$39321194330675250000000$$ $$[]$$ $$744629760$$ $$4.4561$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 379050.2.a.i

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 