Show commands:
SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 370.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
370.b1 | 370a3 | \([1, -1, 0, -395, -2925]\) | \(6825481747209/46250\) | \(46250\) | \([2]\) | \(64\) | \(0.076511\) | |
370.b2 | 370a2 | \([1, -1, 0, -25, -39]\) | \(1767172329/136900\) | \(136900\) | \([2, 2]\) | \(32\) | \(-0.27006\) | |
370.b3 | 370a1 | \([1, -1, 0, -5, 5]\) | \(15438249/2960\) | \(2960\) | \([2]\) | \(16\) | \(-0.61664\) | \(\Gamma_0(N)\)-optimal |
370.b4 | 370a4 | \([1, -1, 0, 25, -209]\) | \(1689410871/18741610\) | \(-18741610\) | \([2]\) | \(64\) | \(0.076511\) |
Rank
sage: E.rank()
The elliptic curves in class 370.b have rank \(1\).
Complex multiplication
The elliptic curves in class 370.b do not have complex multiplication.Modular form 370.2.a.b
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.