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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 130130.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 130130.u1 | 130130u4 | \([1, -1, 0, -2143205, -1207021425]\) | \(225556243796789361/21650378750\) | \(104502243003908750\) | \([2]\) | \(2064384\) | \(2.3021\) | |
| 130130.u2 | 130130u3 | \([1, -1, 0, -794585, 259628851]\) | \(11494365229496241/628112655170\) | \(3031779816988452530\) | \([2]\) | \(2064384\) | \(2.3021\) | |
| 130130.u3 | 130130u2 | \([1, -1, 0, -143935, -15856359]\) | \(68322623117841/16933816900\) | \(81736299817272100\) | \([2, 2]\) | \(1032192\) | \(1.9555\) | |
| 130130.u4 | 130130u1 | \([1, -1, 0, 21685, -1579915]\) | \(233631077679/357076720\) | \(-1723541125786480\) | \([2]\) | \(516096\) | \(1.6089\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 130130.u have rank \(0\).
Complex multiplication
The elliptic curves in class 130130.u do not have complex multiplication.Modular form 130130.2.a.u
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.
