Properties

 Label 3600bf Number of curves 8 Conductor 3600 CM no Rank 1 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("3600.u1")

sage: E.isogeny_class()

Elliptic curves in class 3600bf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3600.u7 3600bf1 [0, 0, 0, -75, 40250] [2] 3072 $$\Gamma_0(N)$$-optimal
3600.u6 3600bf2 [0, 0, 0, -18075, 922250] [2, 2] 6144
3600.u5 3600bf3 [0, 0, 0, -36075, -1219750] [2, 2] 12288
3600.u4 3600bf4 [0, 0, 0, -288075, 59512250] [4] 12288
3600.u2 3600bf5 [0, 0, 0, -486075, -130369750] [2, 2] 24576
3600.u8 3600bf6 [0, 0, 0, 125925, -9157750] [2] 24576
3600.u1 3600bf7 [0, 0, 0, -7776075, -8346199750] [2] 49152
3600.u3 3600bf8 [0, 0, 0, -396075, -180139750] [2] 49152

Rank

sage: E.rank()

The elliptic curves in class 3600bf have rank $$1$$.

Modular form3600.2.a.u

sage: E.q_eigenform(10)

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

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 Cremona numbering.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 2 & 2 & 4 & 4 \\ 4 & 2 & 4 & 1 & 8 & 8 & 16 & 16 \\ 8 & 4 & 2 & 8 & 1 & 4 & 2 & 2 \\ 8 & 4 & 2 & 8 & 4 & 1 & 8 & 8 \\ 16 & 8 & 4 & 16 & 2 & 8 & 1 & 4 \\ 16 & 8 & 4 & 16 & 2 & 8 & 4 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with Cremona labels.