Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 6422.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6422.h1 | 6422f3 | \([1, 0, 0, -14453, -5380831]\) | \(-69173457625/2550136832\) | \(-12309023411929088\) | \([]\) | \(36936\) | \(1.7676\) | |
6422.h2 | 6422f1 | \([1, 0, 0, -2623, 51505]\) | \(-413493625/152\) | \(-733674968\) | \([]\) | \(4104\) | \(0.66903\) | \(\Gamma_0(N)\)-optimal |
6422.h3 | 6422f2 | \([1, 0, 0, 1602, 196676]\) | \(94196375/3511808\) | \(-16950826460672\) | \([]\) | \(12312\) | \(1.2183\) |
Rank
sage: E.rank()
The elliptic curves in class 6422.h have rank \(0\).
Complex multiplication
The elliptic curves in class 6422.h do not have complex multiplication.Modular form 6422.2.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 LMFDB numbering.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.