Show commands:
SageMath
E = EllipticCurve("px1")
E.isogeny_class()
Elliptic curves in class 435600.px
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
435600.px1 | 435600px1 | \([0, 0, 0, -1543575, -738130250]\) | \(104795188976/1875\) | \(7277242500000000\) | \([2]\) | \(5898240\) | \(2.1706\) | \(\Gamma_0(N)\)-optimal |
435600.px2 | 435600px2 | \([0, 0, 0, -1494075, -787679750]\) | \(-23758298924/3515625\) | \(-54579318750000000000\) | \([2]\) | \(11796480\) | \(2.5171\) |
Rank
sage: E.rank()
The elliptic curves in class 435600.px have rank \(0\).
Complex multiplication
The elliptic curves in class 435600.px do not have complex multiplication.Modular form 435600.2.a.px
sage: E.q_eigenform(10)
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 LMFDB 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 LMFDB labels.