Properties

 Label 141960ci Number of curves $6$ Conductor $141960$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("141960.r1")

sage: E.isogeny_class()

Elliptic curves in class 141960ci

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141960.r4 141960ci1 [0, -1, 0, -29631, 1973100] [2] 294912 $$\Gamma_0(N)$$-optimal
141960.r3 141960ci2 [0, -1, 0, -30476, 1855476] [2, 2] 589824
141960.r5 141960ci3 [0, -1, 0, 40504, 9152220] [2] 1179648
141960.r2 141960ci4 [0, -1, 0, -114976, -12982724] [2, 2] 1179648
141960.r6 141960ci5 [0, -1, 0, 189224, -70294004] [2] 2359296
141960.r1 141960ci6 [0, -1, 0, -1771176, -906668244] [2] 2359296

Rank

sage: E.rank()

The elliptic curves in class 141960ci have rank $$0$$.

Modular form 141960.2.a.r

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + q^{7} + q^{9} + 4q^{11} + q^{15} + 2q^{17} + 4q^{19} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.