Show commands:
SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 141120p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141120.kf1 | 141120p1 | \([0, 0, 0, -8652, -118384]\) | \(1092727/540\) | \(35396093214720\) | \([2]\) | \(294912\) | \(1.2929\) | \(\Gamma_0(N)\)-optimal |
141120.kf2 | 141120p2 | \([0, 0, 0, 31668, -908656]\) | \(53582633/36450\) | \(-2389236291993600\) | \([2]\) | \(589824\) | \(1.6395\) |
Rank
sage: E.rank()
The elliptic curves in class 141120p have rank \(1\).
Complex multiplication
The elliptic curves in class 141120p do not have complex multiplication.Modular form 141120.2.a.p
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.