# Properties

 Label 176400.le Number of curves $4$ Conductor $176400$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("176400.le1")

sage: E.isogeny_class()

## Elliptic curves in class 176400.le

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
176400.le1 176400kc3 [0, 0, 0, -18555075, -30725682750] [2] 7962624
176400.le2 176400kc4 [0, 0, 0, -13263075, -48617934750] [2] 15925248
176400.le3 176400kc1 [0, 0, 0, -915075, 295237250] [2] 2654208 $$\Gamma_0(N)$$-optimal
176400.le4 176400kc2 [0, 0, 0, 1436925, 1562965250] [2] 5308416

## Rank

sage: E.rank()

The elliptic curves in class 176400.le have rank $$1$$.

## Modular form 176400.2.a.le

sage: E.q_eigenform(10)

$$q + 2q^{13} + 2q^{19} + O(q^{20})$$

## 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.