Show commands:
SageMath
E = EllipticCurve("he1")
E.isogeny_class()
Elliptic curves in class 141120.he
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141120.he1 | 141120eo2 | \([0, 0, 0, -686028, 218699152]\) | \(544737993463/20000\) | \(1310966415360000\) | \([2]\) | \(1474560\) | \(1.9884\) | |
141120.he2 | 141120eo1 | \([0, 0, 0, -40908, 3745168]\) | \(-115501303/25600\) | \(-1678037011660800\) | \([2]\) | \(737280\) | \(1.6418\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141120.he have rank \(0\).
Complex multiplication
The elliptic curves in class 141120.he do not have complex multiplication.Modular form 141120.2.a.he
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.