Properties

 Label 346560dr Number of curves $2$ Conductor $346560$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("dr1")

sage: E.isogeny_class()

Elliptic curves in class 346560dr

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
346560.dr2 346560dr1 $$[0, -1, 0, -14465, 694305]$$ $$-186169411/6480$$ $$-11651336110080$$ $$$$ $$737280$$ $$1.2801$$ $$\Gamma_0(N)$$-optimal
346560.dr1 346560dr2 $$[0, -1, 0, -233345, 43463457]$$ $$781484460931/900$$ $$1618241126400$$ $$$$ $$1474560$$ $$1.6267$$

Rank

sage: E.rank()

The elliptic curves in class 346560dr have rank $$1$$.

Complex multiplication

The elliptic curves in class 346560dr do not have complex multiplication.

Modular form 346560.2.a.dr

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} - 2 q^{7} + q^{9} + 2 q^{13} - q^{15} - 6 q^{17} + O(q^{20})$$ 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. 