# Properties

 Label 277200.jq Number of curves $6$ Conductor $277200$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("jq1")

sage: E.isogeny_class()

## Elliptic curves in class 277200.jq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
277200.jq1 277200jq6 [0, 0, 0, -10977120075, -442670657687750] [2] 94371840
277200.jq2 277200jq4 [0, 0, 0, -686070075, -6916727537750] [2, 2] 47185920
277200.jq3 277200jq5 [0, 0, 0, -682668075, -6988717259750] [2] 94371840
277200.jq4 277200jq3 [0, 0, 0, -91602075, 177951690250] [2] 47185920
277200.jq5 277200jq2 [0, 0, 0, -43092075, -106947539750] [2, 2] 23592960
277200.jq6 277200jq1 [0, 0, 0, 125925, -4996277750] [2] 11796480 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 277200.2.a.jq

sage: E.q_eigenform(10)

$$q + q^{7} - q^{11} + 2q^{13} + 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.