# Properties

 Label 103488.ih Number of curves 4 Conductor 103488 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("103488.ih1")

sage: E.isogeny_class()

## Elliptic curves in class 103488.ih

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
103488.ih1 103488in4 [0, 1, 0, -92577, 10809567] [2] 393216
103488.ih2 103488in2 [0, 1, 0, -6337, 133055] [2, 2] 196608
103488.ih3 103488in1 [0, 1, 0, -2417, -44913] [2] 98304 $$\Gamma_0(N)$$-optimal
103488.ih4 103488in3 [0, 1, 0, 17183, 909215] [2] 393216

## Rank

sage: E.rank()

The elliptic curves in class 103488.ih have rank $$1$$.

## Modular form 103488.2.a.ih

sage: E.q_eigenform(10)

$$q + q^{3} + 2q^{5} + q^{9} + q^{11} + 2q^{13} + 2q^{15} - 6q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.