Properties

 Label 121275en Number of curves $6$ Conductor $121275$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("en1")

sage: E.isogeny_class()

Elliptic curves in class 121275en

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
121275.bt6 121275en1 [1, -1, 1, 385645, -26777022478] [2] 8847360 $$\Gamma_0(N)$$-optimal
121275.bt5 121275en2 [1, -1, 1, -131969480, -573138978478] [2, 2] 17694720
121275.bt4 121275en3 [1, -1, 1, -280531355, 953779972772] [2] 35389440
121275.bt2 121275en4 [1, -1, 1, -2101089605, -37068811375228] [2, 2] 35389440
121275.bt3 121275en5 [1, -1, 1, -2090670980, -37454633896228] [2] 70778880
121275.bt1 121275en6 [1, -1, 1, -33617430230, -2372429651687728] [2] 70778880

Rank

sage: E.rank()

The elliptic curves in class 121275en have rank $$0$$.

Complex multiplication

The elliptic curves in class 121275en do not have complex multiplication.

Modular form 121275.2.a.en

sage: E.q_eigenform(10)

$$q - q^{2} - q^{4} + 3q^{8} + q^{11} - 2q^{13} - q^{16} - 2q^{17} - 4q^{19} + O(q^{20})$$

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.