Properties

 Label 39600.f Number of curves 4 Conductor 39600 CM no Rank 1 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("39600.f1")

sage: E.isogeny_class()

Elliptic curves in class 39600.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
39600.f1 39600dl4 [0, 0, 0, -1597575, -777212750] [2] 497664
39600.f2 39600dl3 [0, 0, 0, -100200, -12054125] [2] 248832
39600.f3 39600dl2 [0, 0, 0, -22575, -737750] [2] 165888
39600.f4 39600dl1 [0, 0, 0, -10200, 388375] [2] 82944 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 39600.f have rank $$1$$.

Modular form 39600.2.a.f

sage: E.q_eigenform(10)

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

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.