Properties

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

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

Elliptic curves in class 97020.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97020.a1 97020h1 $$[0, 0, 0, -21168, 1083537]$$ $$28311552/2695$$ $$99852348713040$$ $$[2]$$ $$387072$$ $$1.4241$$ $$\Gamma_0(N)$$-optimal
97020.a2 97020h2 $$[0, 0, 0, 25137, 5167638]$$ $$2963088/21175$$ $$-12552866695353600$$ $$[2]$$ $$774144$$ $$1.7707$$

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form 97020.2.a.a

sage: E.q_eigenform(10)

$$q - q^{5} - q^{11} - 6q^{13} + 2q^{17} - 8q^{19} + O(q^{20})$$

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.