Properties

 Label 13860.t Number of curves $4$ Conductor $13860$ CM no Rank $0$ Graph

Related objects

Show commands: SageMath
sage: E = EllipticCurve("t1")

sage: E.isogeny_class()

Elliptic curves in class 13860.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13860.t1 13860f3 $$[0, 0, 0, -59832, -5633091]$$ $$75216478666752/326095$$ $$102696446160$$ $$[2]$$ $$31104$$ $$1.3198$$
13860.t2 13860f4 $$[0, 0, 0, -58887, -5819634]$$ $$-4481782160112/310023175$$ $$-1562159655302400$$ $$[2]$$ $$62208$$ $$1.6663$$
13860.t3 13860f1 $$[0, 0, 0, -1032, -1031]$$ $$281370820608/161767375$$ $$69883506000$$ $$[6]$$ $$10368$$ $$0.77046$$ $$\Gamma_0(N)$$-optimal
13860.t4 13860f2 $$[0, 0, 0, 4113, -8234]$$ $$1113258734352/648484375$$ $$-4482324000000$$ $$[6]$$ $$20736$$ $$1.1170$$

Rank

sage: E.rank()

The elliptic curves in class 13860.t have rank $$0$$.

Complex multiplication

The elliptic curves in class 13860.t do not have complex multiplication.

Modular form 13860.2.a.t

sage: E.q_eigenform(10)

$$q + q^{5} + q^{7} - q^{11} + 2q^{13} + 6q^{17} - 4q^{19} + O(q^{20})$$

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.