Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 31958h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
31958.j2 | 31958h1 | \([1, 1, 1, -13053, 568747]\) | \(-413493625/152\) | \(-90413144792\) | \([]\) | \(45864\) | \(1.0702\) | \(\Gamma_0(N)\)-optimal |
31958.j3 | 31958h2 | \([1, 1, 1, 7972, 2185149]\) | \(94196375/3511808\) | \(-2088905297274368\) | \([]\) | \(137592\) | \(1.6195\) | |
31958.j1 | 31958h3 | \([1, 1, 1, -71923, -59749455]\) | \(-69173457625/2550136832\) | \(-1516880859414659072\) | \([]\) | \(412776\) | \(2.1688\) |
Rank
sage: E.rank()
The elliptic curves in class 31958h have rank \(0\).
Complex multiplication
The elliptic curves in class 31958h do not have complex multiplication.Modular form 31958.2.a.h
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.