Properties

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

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("75150.x1")

sage: E.isogeny_class()

Elliptic curves in class 75150q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
75150.x2 75150q1 [1, -1, 0, 161208, -228144884] [2] 2064384 $$\Gamma_0(N)$$-optimal
75150.x1 75150q2 [1, -1, 0, -4759542, -3835054634] [2] 4128768

Rank

sage: E.rank()

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

Modular form 75150.2.a.x

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + 4q^{7} - q^{8} - 4q^{11} + 4q^{13} - 4q^{14} + q^{16} + 4q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with Cremona labels.