# Properties

 Label 53235g Number of curves $3$ Conductor $53235$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 53235g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53235.q2 53235g1 $$[0, 0, 1, -2028, -38997]$$ $$-262144/35$$ $$-123156031635$$ $$[]$$ $$41040$$ $$0.86063$$ $$\Gamma_0(N)$$-optimal
53235.q3 53235g2 $$[0, 0, 1, 13182, 99414]$$ $$71991296/42875$$ $$-150866138752875$$ $$[]$$ $$123120$$ $$1.4099$$
53235.q1 53235g3 $$[0, 0, 1, -199758, 35947863]$$ $$-250523582464/13671875$$ $$-48107824857421875$$ $$[]$$ $$369360$$ $$1.9592$$

## Rank

sage: E.rank()

The elliptic curves in class 53235g have rank $$0$$.

## Complex multiplication

The elliptic curves in class 53235g do not have complex multiplication.

## Modular form 53235.2.a.g

sage: E.q_eigenform(10)

$$q - 2q^{4} - q^{5} - q^{7} - 3q^{11} + 4q^{16} - 3q^{17} - 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.