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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 7920.bm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7920.bm1 | 7920x3 | \([0, 0, 0, -225747, -8744814]\) | \(15781142246787/8722841600\) | \(703249167207628800\) | \([2]\) | \(124416\) | \(2.1151\) | |
| 7920.bm2 | 7920x1 | \([0, 0, 0, -171747, -27395614]\) | \(5066026756449723/11000000\) | \(1216512000000\) | \([2]\) | \(41472\) | \(1.5657\) | \(\Gamma_0(N)\)-optimal |
| 7920.bm3 | 7920x2 | \([0, 0, 0, -169827, -28038046]\) | \(-4898016158612283/236328125000\) | \(-26136000000000000\) | \([2]\) | \(82944\) | \(1.9123\) | |
| 7920.bm4 | 7920x4 | \([0, 0, 0, 880173, -69128046]\) | \(935355271080573/566899520000\) | \(-45704328200847360000\) | \([2]\) | \(248832\) | \(2.4616\) |
Rank
sage: E.rank()
The elliptic curves in class 7920.bm have rank \(0\).
Complex multiplication
The elliptic curves in class 7920.bm do not have complex multiplication.Modular form 7920.2.a.bm
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
