Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 361920.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
361920.g1 | 361920g2 | \([0, -1, 0, -156884681, 659038556745]\) | \(104257038399293776070517184/14532769730198987776665\) | \(59526224814895053933219840\) | \([2]\) | \(120913920\) | \(3.6721\) | |
361920.g2 | 361920g1 | \([0, -1, 0, 15833644, 55111661550]\) | \(6859403317104911965087424/24475231937622520176525\) | \(-1566414844007841291297600\) | \([2]\) | \(60456960\) | \(3.3255\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 361920.g have rank \(1\).
Complex multiplication
The elliptic curves in class 361920.g do not have complex multiplication.Modular form 361920.2.a.g
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.