# Properties

 Label 227430.fu Number of curves $8$ Conductor $227430$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("227430.fu1")

sage: E.isogeny_class()

## Elliptic curves in class 227430.fu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
227430.fu1 227430h7 [1, -1, 1, -20959367, 23241143409] [2] 31850496
227430.fu2 227430h4 [1, -1, 1, -18717557, 31173602901] [2] 10616832
227430.fu3 227430h6 [1, -1, 1, -8775617, -9737831091] [2, 2] 15925248
227430.fu4 227430h3 [1, -1, 1, -8710637, -9892977339] [2] 7962624
227430.fu5 227430h2 [1, -1, 1, -1172957, 484588581] [2, 2] 5308416
227430.fu6 227430h5 [1, -1, 1, -263237, 1216367349] [2] 10616832
227430.fu7 227430h1 [1, -1, 1, -133277, -6556251] [2] 2654208 $$\Gamma_0(N)$$-optimal
227430.fu8 227430h8 [1, -1, 1, 2368453, -32788225479] [2] 31850496

## Rank

sage: E.rank()

The elliptic curves in class 227430.fu have rank $$0$$.

## Modular form 227430.2.a.fu

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.