# Properties

 Label 176400fd Number of curves 4 Conductor 176400 CM no Rank 2 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("176400.id1")

sage: E.isogeny_class()

## Elliptic curves in class 176400fd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
176400.id3 176400fd1 [0, 0, 0, -444675, -108130750]  2359296 $$\Gamma_0(N)$$-optimal
176400.id2 176400fd2 [0, 0, 0, -1326675, 453703250] [2, 2] 4718592
176400.id1 176400fd3 [0, 0, 0, -19848675, 34034089250]  9437184
176400.id4 176400fd4 [0, 0, 0, 3083325, 2830693250]  9437184

## Rank

sage: E.rank()

The elliptic curves in class 176400fd have rank $$2$$.

## Modular form 176400.2.a.id

sage: E.q_eigenform(10)

$$q - 6q^{13} - 2q^{17} - 8q^{19} + O(q^{20})$$

## 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. 