Show commands:
SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 54096b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54096.z2 | 54096b1 | \([0, -1, 0, -76848, -15279984]\) | \(-416618810500/598934007\) | \(-72155122677292032\) | \([2]\) | \(516096\) | \(1.9269\) | \(\Gamma_0(N)\)-optimal |
54096.z1 | 54096b2 | \([0, -1, 0, -1505688, -710267760]\) | \(1566789944863250/925924041\) | \(223096908799199232\) | \([2]\) | \(1032192\) | \(2.2735\) |
Rank
sage: E.rank()
The elliptic curves in class 54096b have rank \(0\).
Complex multiplication
The elliptic curves in class 54096b do not have complex multiplication.Modular form 54096.2.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 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.