Properties

 Label 97020.d Number of curves $4$ Conductor $97020$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

Elliptic curves in class 97020.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
97020.d1 97020f3 $$[0, 0, 0, -2931768, 1932150213]$$ $$75216478666752/326095$$ $$12082134194277840$$ $$[2]$$ $$1492992$$ $$2.2927$$
97020.d2 97020f4 $$[0, 0, 0, -2885463, 1996134462]$$ $$-4481782160112/310023175$$ $$-183786521286672057600$$ $$[2]$$ $$2985984$$ $$2.6393$$
97020.d3 97020f1 $$[0, 0, 0, -50568, 353633]$$ $$281370820608/161767375$$ $$8221724597394000$$ $$[2]$$ $$497664$$ $$1.7434$$ $$\Gamma_0(N)$$-optimal
97020.d4 97020f2 $$[0, 0, 0, 201537, 2824262]$$ $$1113258734352/648484375$$ $$-527340936276000000$$ $$[2]$$ $$995328$$ $$2.0900$$

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form 97020.2.a.d

sage: E.q_eigenform(10)

$$q - q^{5} - q^{11} - 2q^{13} - 6q^{17} + 4q^{19} + O(q^{20})$$

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 LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.