Properties

 Label 227430fd Number of curves $4$ Conductor $227430$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("227430.i1")

sage: E.isogeny_class()

Elliptic curves in class 227430fd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
227430.i3 227430fd1 [1, -1, 0, -42813765, -107800072619] [2] 17694720 $$\Gamma_0(N)$$-optimal
227430.i2 227430fd2 [1, -1, 0, -46972485, -85591676075] [2, 2] 35389440
227430.i1 227430fd3 [1, -1, 0, -288958005, 1824593621701] [2] 70778880
227430.i4 227430fd4 [1, -1, 0, 128473515, -574489499675] [2] 70778880

Rank

sage: E.rank()

The elliptic curves in class 227430fd have rank $$1$$.

Modular form 227430.2.a.i

sage: E.q_eigenform(10)

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

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 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.