Properties

 Label 68544.t Number of curves $6$ Conductor $68544$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("68544.t1")

sage: E.isogeny_class()

Elliptic curves in class 68544.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
68544.t1 68544dq6 [0, 0, 0, -7901915916, -270362650933744] [2] 47185920
68544.t2 68544dq4 [0, 0, 0, -494809356, -4207535177200] [2, 2] 23592960
68544.t3 68544dq5 [0, 0, 0, -168539916, -9673331343856] [2] 47185920
68544.t4 68544dq2 [0, 0, 0, -52257036, 36541571600] [2, 2] 11796480
68544.t5 68544dq1 [0, 0, 0, -40460556, 98935513616] [2] 5898240 $$\Gamma_0(N)$$-optimal
68544.t6 68544dq3 [0, 0, 0, 201551604, 287406031376] [2] 23592960

Rank

sage: E.rank()

The elliptic curves in class 68544.t have rank $$1$$.

Modular form 68544.2.a.t

sage: E.q_eigenform(10)

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.