Properties

 Label 265200e Number of curves 2 Conductor 265200 CM no Rank 1 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("265200.e1")

sage: E.isogeny_class()

Elliptic curves in class 265200e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
265200.e2 265200e1 [0, -1, 0, -3933, -84888] [2] 442368 $$\Gamma_0(N)$$-optimal
265200.e1 265200e2 [0, -1, 0, -61308, -5822388] [2] 884736

Rank

sage: E.rank()

The elliptic curves in class 265200e have rank $$1$$.

Modular form 265200.2.a.e

sage: E.q_eigenform(10)

$$q - q^{3} - 4q^{7} + q^{9} - 2q^{11} + q^{13} - q^{17} - 2q^{19} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.