Show commands:
SageMath
E = EllipticCurve("zu1")
E.isogeny_class()
Elliptic curves in class 705600.zu
sage: E.isogeny_class().curves
LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
---|---|---|---|---|---|---|
705600.zu1 | \([0, 0, 0, -622706700, 5980987726000]\) | \(608119035935048/826875\) | \(36309944986560000000000\) | \([2]\) | \(113246208\) | \(3.6031\) |
705600.zu2 | \([0, 0, 0, -98798700, -252517286000]\) | \(2428799546888/778248135\) | \(34174629741790379520000000\) | \([2]\) | \(113246208\) | \(3.6031\) |
705600.zu3 | \([0, 0, 0, -39263700, 91714084000]\) | \(1219555693504/43758225\) | \(240190286086094400000000\) | \([2, 2]\) | \(56623104\) | \(3.2565\) |
705600.zu4 | \([0, 0, 0, 922425, 5072798500]\) | \(1012048064/130203045\) | \(-11167010112038445000000\) | \([2]\) | \(28311552\) | \(2.9100\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.zu have rank \(1\).
Complex multiplication
The elliptic curves in class 705600.zu do not have complex multiplication.Modular form 705600.2.a.zu
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.