# Properties

 Label 177450.cb Number of curves $8$ Conductor $177450$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cb1")

sage: E.isogeny_class()

## Elliptic curves in class 177450.cb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
177450.cb1 177450iz8 [1, 1, 0, -1483957400, -22003535520000] [2] 63700992
177450.cb2 177450iz6 [1, 1, 0, -92749400, -343818168000] [2, 2] 31850496
177450.cb3 177450iz7 [1, 1, 0, -85989400, -396052688000] [2] 63700992
177450.cb4 177450iz5 [1, 1, 0, -18410525, -29878254375] [2] 21233664
177450.cb5 177450iz3 [1, 1, 0, -6221400, -4541880000] [2] 15925248
177450.cb6 177450iz2 [1, 1, 0, -2440025, 769135125] [2, 2] 10616832
177450.cb7 177450iz1 [1, 1, 0, -2102025, 1171693125] [2] 5308416 $$\Gamma_0(N)$$-optimal
177450.cb8 177450iz4 [1, 1, 0, 8122475, 5659572625] [2] 21233664

## Rank

sage: E.rank()

The elliptic curves in class 177450.cb have rank $$0$$.

## Complex multiplication

The elliptic curves in class 177450.cb do not have complex multiplication.

## Modular form 177450.2.a.cb

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.