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SageMath
E = EllipticCurve("ew1")
E.isogeny_class()
Elliptic curves in class 179520ew
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 179520.hj4 | 179520ew1 | \([0, 1, 0, -1825, 111935]\) | \(-2565726409/19388160\) | \(-5082489815040\) | \([2]\) | \(393216\) | \(1.1211\) | \(\Gamma_0(N)\)-optimal |
| 179520.hj3 | 179520ew2 | \([0, 1, 0, -47905, 4010303]\) | \(46380496070089/125888400\) | \(33000888729600\) | \([2, 2]\) | \(786432\) | \(1.4676\) | |
| 179520.hj1 | 179520ew3 | \([0, 1, 0, -765985, 257779775]\) | \(189602977175292169/1402500\) | \(367656960000\) | \([2]\) | \(1572864\) | \(1.8142\) | |
| 179520.hj2 | 179520ew4 | \([0, 1, 0, -67105, 473663]\) | \(127483771761289/73369857660\) | \(19233467966423040\) | \([2]\) | \(1572864\) | \(1.8142\) |
Rank
sage: E.rank()
The elliptic curves in class 179520ew have rank \(0\).
Complex multiplication
The elliptic curves in class 179520ew do not have complex multiplication.Modular form 179520.2.a.ew
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
