# Properties

 Label 176400.tn Number of curves $2$ Conductor $176400$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("tn1")

sage: E.isogeny_class()

## Elliptic curves in class 176400.tn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
176400.tn1 176400gy2 $$[0, 0, 0, -61831875, 198003181250]$$ $$-7620530425/526848$$ $$-1807428372664320000000000$$ $$[]$$ $$29859840$$ $$3.4054$$
176400.tn2 176400gy1 $$[0, 0, 0, 4318125, 280831250]$$ $$2595575/1512$$ $$-5187134998080000000000$$ $$[]$$ $$9953280$$ $$2.8561$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 176400.tn have rank $$0$$.

## Complex multiplication

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

## Modular form 176400.2.a.tn

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. 