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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 154560bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 154560.ef3 | 154560bt1 | \([0, 1, 0, -30721, -117995521]\) | \(-12232183057921/22933241856000\) | \(-6011811753099264000\) | \([2]\) | \(3981312\) | \(2.2823\) | \(\Gamma_0(N)\)-optimal |
| 154560.ef2 | 154560bt2 | \([0, 1, 0, -3799041, -2816866305]\) | \(23131609187144855041/322060536000000\) | \(84426237149184000000\) | \([2]\) | \(7962624\) | \(2.6289\) | |
| 154560.ef4 | 154560bt3 | \([0, 1, 0, 276479, 3184834559]\) | \(8915971454369279/16719623332762560\) | \(-4382948938943708528640\) | \([2]\) | \(11943936\) | \(2.8316\) | |
| 154560.ef1 | 154560bt4 | \([0, 1, 0, -30871041, 64601514495]\) | \(12411881707829361287041/303132494474220600\) | \(79464364631450084966400\) | \([2]\) | \(23887872\) | \(3.1782\) |
Rank
sage: E.rank()
The elliptic curves in class 154560bt have rank \(0\).
Complex multiplication
The elliptic curves in class 154560bt do not have complex multiplication.Modular form 154560.2.a.bt
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.
