Show commands:
SageMath
E = EllipticCurve("km1")
E.isogeny_class()
Elliptic curves in class 141120.km
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141120.km1 | 141120it1 | \([0, 0, 0, -75852, 8040816]\) | \(-5154200289/20\) | \(-187280916480\) | \([]\) | \(322560\) | \(1.3762\) | \(\Gamma_0(N)\)-optimal |
141120.km2 | 141120it2 | \([0, 0, 0, 528948, -76292496]\) | \(1747829720511/1280000000\) | \(-11985978654720000000\) | \([]\) | \(2257920\) | \(2.3492\) |
Rank
sage: E.rank()
The elliptic curves in class 141120.km have rank \(0\).
Complex multiplication
The elliptic curves in class 141120.km do not have complex multiplication.Modular form 141120.2.a.km
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.