Show commands:
SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 12600.cb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12600.cb1 | 12600d2 | \([0, 0, 0, -24975, -1518750]\) | \(21882096/7\) | \(551124000000\) | \([2]\) | \(24576\) | \(1.2277\) | |
12600.cb2 | 12600d1 | \([0, 0, 0, -1350, -30375]\) | \(-55296/49\) | \(-241116750000\) | \([2]\) | \(12288\) | \(0.88115\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 12600.cb have rank \(0\).
Complex multiplication
The elliptic curves in class 12600.cb do not have complex multiplication.Modular form 12600.2.a.cb
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.