Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 244398.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
244398.g1 | 244398g3 | \([1, 1, 0, -119829, 15909387]\) | \(1285429208617/614922\) | \(91030524935658\) | \([2]\) | \(1576960\) | \(1.6334\) | |
244398.g2 | 244398g4 | \([1, 1, 0, -66929, -6581577]\) | \(223980311017/4278582\) | \(633383690029398\) | \([2]\) | \(1576960\) | \(1.6334\) | |
244398.g3 | 244398g2 | \([1, 1, 0, -8739, 156825]\) | \(498677257/213444\) | \(31597372291716\) | \([2, 2]\) | \(788480\) | \(1.2868\) | |
244398.g4 | 244398g1 | \([1, 1, 0, 1841, 19285]\) | \(4657463/3696\) | \(-547140645744\) | \([2]\) | \(394240\) | \(0.94026\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 244398.g have rank \(0\).
Complex multiplication
The elliptic curves in class 244398.g do not have complex multiplication.Modular form 244398.2.a.g
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.