Properties

 Label 107712bs Number of curves $2$ Conductor $107712$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bs1")

sage: E.isogeny_class()

Elliptic curves in class 107712bs

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
107712.l1 107712bs1 [0, 0, 0, -520716, -143483920] [2] 1720320 $$\Gamma_0(N)$$-optimal
107712.l2 107712bs2 [0, 0, 0, -152076, -342696976] [2] 3440640

Rank

sage: E.rank()

The elliptic curves in class 107712bs have rank $$1$$.

Complex multiplication

The elliptic curves in class 107712bs do not have complex multiplication.

Modular form 107712.2.a.bs

sage: E.q_eigenform(10)

$$q - 2q^{5} - 4q^{7} - q^{11} + 4q^{13} + q^{17} + 8q^{19} + O(q^{20})$$

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.