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SageMath
E = EllipticCurve("df1")
E.isogeny_class()
Elliptic curves in class 124950df
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 124950.cn4 | 124950df1 | \([1, 0, 1, 19139374, -10833517852]\) | \(421792317902132351/271682182840320\) | \(-499424017640325120000000\) | \([2]\) | \(20643840\) | \(3.2362\) | \(\Gamma_0(N)\)-optimal |
| 124950.cn3 | 124950df2 | \([1, 0, 1, -81212626, -89108077852]\) | \(32224493437735955329/16782725759385600\) | \(30851107857280569600000000\) | \([2, 2]\) | \(41287680\) | \(3.5828\) | |
| 124950.cn2 | 124950df3 | \([1, 0, 1, -734284626, 7593630930148]\) | \(23818189767728437646209/232359312482640000\) | \(427138136785470521250000000\) | \([2]\) | \(82575360\) | \(3.9294\) | |
| 124950.cn1 | 124950df4 | \([1, 0, 1, -1033772626, -12781017517852]\) | \(66464620505913166201729/74880071980801920\) | \(137649462319833829470000000\) | \([2]\) | \(82575360\) | \(3.9294\) |
Rank
sage: E.rank()
The elliptic curves in class 124950df have rank \(0\).
Complex multiplication
The elliptic curves in class 124950df do not have complex multiplication.Modular form 124950.2.a.df
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.
