Show commands:
SageMath
E = EllipticCurve("hg1")
E.isogeny_class()
Elliptic curves in class 224400.hg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
224400.hg1 | 224400co1 | \([0, 1, 0, -79208, -8606412]\) | \(858729462625/38148\) | \(2441472000000\) | \([2]\) | \(884736\) | \(1.4543\) | \(\Gamma_0(N)\)-optimal |
224400.hg2 | 224400co2 | \([0, 1, 0, -75208, -9510412]\) | \(-735091890625/181908738\) | \(-11642159232000000\) | \([2]\) | \(1769472\) | \(1.8009\) |
Rank
sage: E.rank()
The elliptic curves in class 224400.hg have rank \(0\).
Complex multiplication
The elliptic curves in class 224400.hg do not have complex multiplication.Modular form 224400.2.a.hg
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.