Properties

 Label 60984ch Number of curves $4$ Conductor $60984$ CM no Rank $1$ Graph

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Show commands: SageMath
sage: E = EllipticCurve("ch1")

sage: E.isogeny_class()

Elliptic curves in class 60984ch

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60984.p4 60984ch1 $$[0, 0, 0, 1089, 71874]$$ $$432/7$$ $$-2314310600448$$ $$[2]$$ $$81920$$ $$1.0531$$ $$\Gamma_0(N)$$-optimal
60984.p3 60984ch2 $$[0, 0, 0, -20691, 1078110]$$ $$740772/49$$ $$64800696812544$$ $$[2, 2]$$ $$163840$$ $$1.3996$$
60984.p2 60984ch3 $$[0, 0, 0, -64251, -4959306]$$ $$11090466/2401$$ $$6350468287629312$$ $$[2]$$ $$327680$$ $$1.7462$$
60984.p1 60984ch4 $$[0, 0, 0, -325611, 71514630]$$ $$1443468546/7$$ $$18514484803584$$ $$[2]$$ $$327680$$ $$1.7462$$

Rank

sage: E.rank()

The elliptic curves in class 60984ch have rank $$1$$.

Complex multiplication

The elliptic curves in class 60984ch do not have complex multiplication.

Modular form 60984.2.a.ch

sage: E.q_eigenform(10)

$$q - 2q^{5} + q^{7} - 2q^{13} - 6q^{17} - 8q^{19} + O(q^{20})$$

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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with Cremona labels.