Show commands:
SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 23400.bp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23400.bp1 | 23400k4 | \([0, 0, 0, -372675, 87236750]\) | \(490757540836/2142075\) | \(24985162800000000\) | \([2]\) | \(294912\) | \(1.9993\) | |
| 23400.bp2 | 23400k2 | \([0, 0, 0, -35175, -175750]\) | \(1650587344/950625\) | \(2772022500000000\) | \([2, 2]\) | \(147456\) | \(1.6528\) | |
| 23400.bp3 | 23400k1 | \([0, 0, 0, -25050, -1522375]\) | \(9538484224/26325\) | \(4797731250000\) | \([2]\) | \(73728\) | \(1.3062\) | \(\Gamma_0(N)\)-optimal |
| 23400.bp4 | 23400k3 | \([0, 0, 0, 140325, -1404250]\) | \(26198797244/15234375\) | \(-177693750000000000\) | \([2]\) | \(294912\) | \(1.9993\) |
Rank
sage: E.rank()
The elliptic curves in class 23400.bp have rank \(0\).
Complex multiplication
The elliptic curves in class 23400.bp do not have complex multiplication.Modular form 23400.2.a.bp
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
