Show commands:
SageMath
E = EllipticCurve("hd1")
E.isogeny_class()
Elliptic curves in class 277200.hd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
277200.hd1 | 277200hd2 | \([0, 0, 0, -15525, 772875]\) | \(-84098304/3773\) | \(-18565989750000\) | \([]\) | \(746496\) | \(1.3105\) | |
277200.hd2 | 277200hd1 | \([0, 0, 0, 975, 2875]\) | \(15185664/9317\) | \(-62889750000\) | \([]\) | \(248832\) | \(0.76122\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 277200.hd have rank \(1\).
Complex multiplication
The elliptic curves in class 277200.hd do not have complex multiplication.Modular form 277200.2.a.hd
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.