# Properties

 Label 58800gr Number of curves $2$ Conductor $58800$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("gr1")

sage: E.isogeny_class()

## Elliptic curves in class 58800gr

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58800.b2 58800gr1 $$[0, -1, 0, -34800208, 78452158912]$$ $$505318200625/4251528$$ $$39214740585484800000000$$ $$[]$$ $$7257600$$ $$3.1607$$ $$\Gamma_0(N)$$-optimal
58800.b1 58800gr2 $$[0, -1, 0, -2813100208, 57429232078912]$$ $$266916252066900625/162$$ $$1494236419200000000$$ $$[]$$ $$21772800$$ $$3.7100$$

## Rank

sage: E.rank()

The elliptic curves in class 58800gr have rank $$1$$.

## Complex multiplication

The elliptic curves in class 58800gr do not have complex multiplication.

## Modular form 58800.2.a.gr

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} - 6q^{11} - 4q^{13} - 3q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.