Properties

 Label 75150bi Number of curves 2 Conductor 75150 CM no Rank 1 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("75150.bh1")

sage: E.isogeny_class()

Elliptic curves in class 75150bi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
75150.bh2 75150bi1 [1, -1, 1, -333005, -318933003] [] 1806336 $$\Gamma_0(N)$$-optimal
75150.bh1 75150bi2 [1, -1, 1, -85619255, 309617914497] [] 12644352

Rank

sage: E.rank()

The elliptic curves in class 75150bi have rank $$1$$.

Modular form 75150.2.a.bh

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{7} + q^{8} + 2q^{11} - q^{14} + q^{16} + 4q^{17} - q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with Cremona labels.