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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 129430l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 129430.f3 | 129430l1 | \([1, -1, 0, -2880164, 1880914000]\) | \(417988868898609/302059520\) | \(1909427888326676480\) | \([2]\) | \(3193344\) | \(2.4427\) | \(\Gamma_0(N)\)-optimal |
| 129430.f2 | 129430l2 | \([1, -1, 0, -3471844, 1052917008]\) | \(732139195216689/348052801600\) | \(2200168119135168078400\) | \([2, 2]\) | \(6386688\) | \(2.7892\) | |
| 129430.f4 | 129430l3 | \([1, -1, 0, 12429556, 7989107688]\) | \(33595399126917711/23807013985720\) | \(-150492778516356621660280\) | \([2]\) | \(12773376\) | \(3.1358\) | |
| 129430.f1 | 129430l4 | \([1, -1, 0, -28840124, -58882181320]\) | \(419666552369006769/5863243715000\) | \(37063692167282487035000\) | \([2]\) | \(12773376\) | \(3.1358\) |
Rank
sage: E.rank()
The elliptic curves in class 129430l have rank \(0\).
Complex multiplication
The elliptic curves in class 129430l do not have complex multiplication.Modular form 129430.2.a.l
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.
