Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 471510.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
471510.g1 | 471510g3 | \([1, -1, 0, -36800880, -85918892500]\) | \(58015885327629867/38728300\) | \(3679424027976680100\) | \([2]\) | \(27869184\) | \(2.8788\) | |
471510.g2 | 471510g4 | \([1, -1, 0, -36572730, -87036964390]\) | \(-56943538625741067/1499881220890\) | \(-142497837582689259916830\) | \([2]\) | \(55738368\) | \(3.2254\) | |
471510.g3 | 471510g1 | \([1, -1, 0, -550380, -64306800]\) | \(141477771269043/68107000000\) | \(8875965975201000000\) | \([2]\) | \(9289728\) | \(2.3295\) | \(\Gamma_0(N)\)-optimal* |
471510.g4 | 471510g2 | \([1, -1, 0, 1984620, -491707800]\) | \(6633333032010957/4638563449000\) | \(-604515414673014507000\) | \([2]\) | \(18579456\) | \(2.6761\) |
Rank
sage: E.rank()
The elliptic curves in class 471510.g have rank \(1\).
Complex multiplication
The elliptic curves in class 471510.g do not have complex multiplication.Modular form 471510.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.