Show commands:
SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 353925bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
353925.bm2 | 353925bm1 | \([0, 0, 1, -3630, 78196]\) | \(163840/13\) | \(419727089925\) | \([]\) | \(388800\) | \(0.97383\) | \(\Gamma_0(N)\)-optimal |
353925.bm1 | 353925bm2 | \([0, 0, 1, -58080, -5372249]\) | \(671088640/2197\) | \(70933878197325\) | \([]\) | \(1166400\) | \(1.5231\) |
Rank
sage: E.rank()
The elliptic curves in class 353925bm have rank \(2\).
Complex multiplication
The elliptic curves in class 353925bm do not have complex multiplication.Modular form 353925.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.