# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("103488.ca1")

sage: E.isogeny_class()

## Elliptic curves in class 103488.ca

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
103488.ca1 103488ff3 [0, -1, 0, -252513, -48568575] [2] 829440
103488.ca2 103488ff4 [0, -1, 0, -127073, -96963327] [2] 1658880
103488.ca3 103488ff1 [0, -1, 0, -17313, 832833] [2] 276480 $$\Gamma_0(N)$$-optimal
103488.ca4 103488ff2 [0, -1, 0, 14047, 3485889] [2] 552960

## Rank

sage: E.rank()

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

## Modular form 103488.2.a.ca

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} - q^{11} - 4q^{13} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.