Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 309738.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
309738.g1 | 309738g1 | \([1, 1, 0, -2084558768, -36672542088576]\) | \(-21293376668673906679951249/26211168887701209984\) | \(-1233127532361693488463275904\) | \([]\) | \(231154560\) | \(4.1080\) | \(\Gamma_0(N)\)-optimal |
309738.g2 | 309738g2 | \([1, 1, 0, 5903465122, 2301501327836394]\) | \(483641001192506212470106511/48918776756543177755473774\) | \(-2301426949953896312045866270224894\) | \([]\) | \(1618081920\) | \(5.0810\) |
Rank
sage: E.rank()
The elliptic curves in class 309738.g have rank \(0\).
Complex multiplication
The elliptic curves in class 309738.g do not have complex multiplication.Modular form 309738.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.