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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 179520.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 179520.f1 | 179520hq4 | \([0, -1, 0, -1849761, -967709535]\) | \(10680482485334708644/317343675\) | \(20797435084800\) | \([2]\) | \(2228224\) | \(2.0625\) | |
| 179520.f2 | 179520hq3 | \([0, -1, 0, -181761, 4129665]\) | \(10133238887216644/5754999888825\) | \(377159672714035200\) | \([2]\) | \(2228224\) | \(2.0625\) | |
| 179520.f3 | 179520hq2 | \([0, -1, 0, -115761, -15049935]\) | \(10471148863450576/56846480625\) | \(931372738560000\) | \([2, 2]\) | \(1114112\) | \(1.7159\) | |
| 179520.f4 | 179520hq1 | \([0, -1, 0, -3261, -492435]\) | \(-3746358409216/100585546875\) | \(-102999600000000\) | \([2]\) | \(557056\) | \(1.3694\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 179520.f have rank \(0\).
Complex multiplication
The elliptic curves in class 179520.f do not have complex multiplication.Modular form 179520.2.a.f
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.
