# Properties

 Label 116380.a Number of curves $4$ Conductor $116380$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 116380.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116380.a1 116380e4 $$[0, 1, 0, -3756076, 2800628724]$$ $$154639330142416/33275$$ $$1261028916857600$$ $$[2]$$ $$2566080$$ $$2.2822$$
116380.a2 116380e3 $$[0, 1, 0, -235581, 43377040]$$ $$610462990336/8857805$$ $$20980368604218320$$ $$[2]$$ $$1283040$$ $$1.9356$$
116380.a3 116380e2 $$[0, 1, 0, -53076, 2641924]$$ $$436334416/171875$$ $$6513579116000000$$ $$[2]$$ $$855360$$ $$1.7329$$
116380.a4 116380e1 $$[0, 1, 0, -23981, -1408100]$$ $$643956736/15125$$ $$35824685138000$$ $$[2]$$ $$427680$$ $$1.3863$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 116380.a have rank $$0$$.

## Complex multiplication

The elliptic curves in class 116380.a do not have complex multiplication.

## Modular form 116380.2.a.a

sage: E.q_eigenform(10)

$$q - 2q^{3} - q^{5} + 4q^{7} + q^{9} + q^{11} - 4q^{13} + 2q^{15} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.