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SageMath
E = EllipticCurve("dt1")
E.isogeny_class()
Elliptic curves in class 465290dt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 465290.dt3 | 465290dt1 | \([1, 1, 1, -43645, 3389395]\) | \(380920459249/12622400\) | \(304674050945600\) | \([2]\) | \(2654208\) | \(1.5522\) | \(\Gamma_0(N)\)-optimal |
| 465290.dt4 | 465290dt2 | \([1, 1, 1, 14155, 11781955]\) | \(12994449551/2489452840\) | \(-60089339697745960\) | \([2]\) | \(5308416\) | \(1.8988\) | |
| 465290.dt1 | 465290dt3 | \([1, 1, 1, -488705, -130565573]\) | \(534774372149809/5323062500\) | \(128485788385062500\) | \([2]\) | \(7962624\) | \(2.1015\) | |
| 465290.dt2 | 465290dt4 | \([1, 1, 1, -127455, -318849073]\) | \(-9486391169809/1813439640250\) | \(-43772024443869552250\) | \([2]\) | \(15925248\) | \(2.4481\) |
Rank
sage: E.rank()
The elliptic curves in class 465290dt have rank \(0\).
Complex multiplication
The elliptic curves in class 465290dt do not have complex multiplication.Modular form 465290.2.a.dt
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
