Show commands:
SageMath
E = EllipticCurve("cm1")
E.isogeny_class()
Elliptic curves in class 254100.cm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 254100.cm1 | 254100cm2 | \([0, 1, 0, -5506508, -4792314012]\) | \(2605772594896/108945375\) | \(772013509921500000000\) | \([2]\) | \(9953280\) | \(2.7728\) | |
| 254100.cm2 | 254100cm1 | \([0, 1, 0, 165367, -277501512]\) | \(1129201664/75796875\) | \(-33569696917968750000\) | \([2]\) | \(4976640\) | \(2.4263\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 254100.cm have rank \(0\).
Complex multiplication
The elliptic curves in class 254100.cm do not have complex multiplication.Modular form 254100.2.a.cm
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.
