Properties

 Label 97020.q Number of curves $2$ Conductor $97020$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("q1")

sage: E.isogeny_class()

Elliptic curves in class 97020.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97020.q1 97020ca2 $$[0, 0, 0, -4884663, 4155261838]$$ $$1711503051568/7425$$ $$55917315279302400$$ $$[2]$$ $$1806336$$ $$2.4204$$
97020.q2 97020ca1 $$[0, 0, 0, -300468, 67076737]$$ $$-6373654528/441045$$ $$-207593032974410160$$ $$[2]$$ $$903168$$ $$2.0738$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 97020.q have rank $$1$$.

Complex multiplication

The elliptic curves in class 97020.q do not have complex multiplication.

Modular form 97020.2.a.q

sage: E.q_eigenform(10)

$$q - q^{5} + q^{11} - 6q^{13} + 2q^{17} + 2q^{19} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.