# Properties

 Label 369600nn Number of curves 4 Conductor 369600 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("369600.nn1")

sage: E.isogeny_class()

## Elliptic curves in class 369600nn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
369600.nn3 369600nn1 [0, 1, 0, -801633, 239608863] [2] 7077888 $$\Gamma_0(N)$$-optimal
369600.nn2 369600nn2 [0, 1, 0, -3393633, -2168359137] [2, 2] 14155776
369600.nn4 369600nn3 [0, 1, 0, 4526367, -10777399137] [2] 28311552
369600.nn1 369600nn4 [0, 1, 0, -52785633, -147627799137] [2] 28311552

## Rank

sage: E.rank()

The elliptic curves in class 369600nn have rank $$1$$.

## Modular form 369600.2.a.nn

sage: E.q_eigenform(10)

$$q + q^{3} - q^{7} + q^{9} - q^{11} + 2q^{13} - 2q^{17} + 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.