# Properties

 Label 3465.l Number of curves $6$ Conductor $3465$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("3465.l1")

sage: E.isogeny_class()

## Elliptic curves in class 3465.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3465.l1 3465e5 [1, -1, 0, -119250, 15879325] [2] 16384
3465.l2 3465e3 [1, -1, 0, -7875, 220000] [2, 2] 8192
3465.l3 3465e2 [1, -1, 0, -2430, -42449] [2, 2] 4096
3465.l4 3465e1 [1, -1, 0, -2385, -44240] [2] 2048 $$\Gamma_0(N)$$-optimal
3465.l5 3465e4 [1, -1, 0, 2295, -190814] [2] 8192
3465.l6 3465e6 [1, -1, 0, 16380, 1292071] [2] 16384

## Rank

sage: E.rank()

The elliptic curves in class 3465.l have rank $$0$$.

## Modular form3465.2.a.l

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} - q^{5} - q^{7} - 3q^{8} - q^{10} - q^{11} - 2q^{13} - q^{14} - q^{16} + 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.