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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 158400bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 158400.lx2 | 158400bo1 | \([0, 0, 0, -7320, -241000]\) | \(464857088/121\) | \(11290752000\) | \([2]\) | \(147456\) | \(0.91407\) | \(\Gamma_0(N)\)-optimal |
| 158400.lx1 | 158400bo2 | \([0, 0, 0, -8220, -178000]\) | \(41141648/14641\) | \(21858895872000\) | \([2]\) | \(294912\) | \(1.2606\) |
Rank
sage: E.rank()
The elliptic curves in class 158400bo have rank \(1\).
Complex multiplication
The elliptic curves in class 158400bo do not have complex multiplication.Modular form 158400.2.a.bo
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
