# Properties

 Label 301665ca Number of curves 4 Conductor 301665 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("301665.ca1")

sage: E.isogeny_class()

## Elliptic curves in class 301665ca

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
301665.ca4 301665ca1 [1, 0, 1, 2362, 74531] [2] 491520 $$\Gamma_0(N)$$-optimal
301665.ca3 301665ca2 [1, 0, 1, -18763, 809681] [2, 2] 983040
301665.ca1 301665ca3 [1, 0, 1, -284938, 58516421] [2] 1966080
301665.ca2 301665ca4 [1, 0, 1, -90588, -9762959] [2] 1966080

## Rank

sage: E.rank()

The elliptic curves in class 301665ca have rank $$1$$.

## Modular form 301665.2.a.ca

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} - q^{4} + q^{5} + q^{6} - q^{7} - 3q^{8} + q^{9} + q^{10} - q^{12} - q^{14} + q^{15} - q^{16} - q^{17} + q^{18} - 4q^{19} + O(q^{20})$$

## 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.