# Properties

 Label 176400.to Number of curves $2$ Conductor $176400$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("to1")

sage: E.isogeny_class()

## Elliptic curves in class 176400.to

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
176400.to1 176400cr2 $$[0, 0, 0, -2473275, 1584025450]$$ $$-7620530425/526848$$ $$-115675415850516480000$$ $$[]$$ $$5971968$$ $$2.6007$$
176400.to2 176400cr1 $$[0, 0, 0, 172725, 2246650]$$ $$2595575/1512$$ $$-331976639877120000$$ $$[]$$ $$1990656$$ $$2.0514$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 176400.to have rank $$1$$.

## Complex multiplication

The elliptic curves in class 176400.to do not have complex multiplication.

## Modular form 176400.2.a.to

sage: E.q_eigenform(10)

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

## 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 LMFDB 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 LMFDB labels.