# Properties

 Label 277200.gt Number of curves $2$ Conductor $277200$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("gt1")

sage: E.isogeny_class()

## Elliptic curves in class 277200.gt

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
277200.gt1 277200gt2 $$[0, 0, 0, -116175, 15214250]$$ $$59466754384/121275$$ $$353637900000000$$ $$[2]$$ $$1474560$$ $$1.6781$$
277200.gt2 277200gt1 $$[0, 0, 0, -4800, 401375]$$ $$-67108864/343035$$ $$-62518128750000$$ $$[2]$$ $$737280$$ $$1.3315$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 277200.gt have rank $$0$$.

## Complex multiplication

The elliptic curves in class 277200.gt do not have complex multiplication.

## Modular form 277200.2.a.gt

sage: E.q_eigenform(10)

$$q - q^{7} + q^{11} + 6q^{13} + 2q^{17} + O(q^{20})$$

## 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.