# Properties

 Label 93058.a Number of curves $2$ Conductor $93058$ CM no Rank $2$ Graph # Learn more

Show commands: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 93058.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
93058.a1 93058b2 $$[1, 0, 1, -174996, 26364434]$$ $$24553362849625/1755162752$$ $$42365362032629888$$ $$$$ $$1032192$$ $$1.9374$$
93058.a2 93058b1 $$[1, 0, 1, 9964, 1801746]$$ $$4533086375/60669952$$ $$-1464425152626688$$ $$$$ $$516096$$ $$1.5908$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 93058.a have rank $$2$$.

## Complex multiplication

The elliptic curves in class 93058.a do not have complex multiplication.

## Modular form 93058.2.a.a

sage: E.q_eigenform(10)

$$q - q^{2} - 2q^{3} + q^{4} + 2q^{6} - q^{7} - q^{8} + q^{9} - 4q^{11} - 2q^{12} + q^{14} + q^{16} - q^{18} - 6q^{19} + O(q^{20})$$ ## 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 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. 