Properties

 Label 35280fj Number of curves $2$ Conductor $35280$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("35280.ev1")

sage: E.isogeny_class()

Elliptic curves in class 35280fj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35280.ev1 35280fj1 [0, 0, 0, -105987, 5075714] [2] 258048 $$\Gamma_0(N)$$-optimal
35280.ev2 35280fj2 [0, 0, 0, 387933, 38958626] [2] 516096

Rank

sage: E.rank()

The elliptic curves in class 35280fj have rank $$1$$.

Modular form 35280.2.a.ev

sage: E.q_eigenform(10)

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

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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with Cremona labels.