Show commands:
SageMath
E = EllipticCurve("ew1")
E.isogeny_class()
Elliptic curves in class 124950ew
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
124950.fo1 | 124950ew1 | \([1, 1, 1, -3088, -43219]\) | \(1771561/612\) | \(1125018562500\) | \([2]\) | \(230400\) | \(1.0141\) | \(\Gamma_0(N)\)-optimal |
124950.fo2 | 124950ew2 | \([1, 1, 1, 9162, -288219]\) | \(46268279/46818\) | \(-86063920031250\) | \([2]\) | \(460800\) | \(1.3607\) |
Rank
sage: E.rank()
The elliptic curves in class 124950ew have rank \(1\).
Complex multiplication
The elliptic curves in class 124950ew do not have complex multiplication.Modular form 124950.2.a.ew
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 Cremona 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 Cremona labels.