Show commands:
SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 299538z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
299538.z1 | 299538z1 | \([1, -1, 1, -11441, -511451]\) | \(-35937/4\) | \(-18433094650884\) | \([]\) | \(943488\) | \(1.2828\) | \(\Gamma_0(N)\)-optimal |
299538.z2 | 299538z2 | \([1, -1, 1, 71764, 719983]\) | \(109503/64\) | \(-23889290667545664\) | \([]\) | \(2830464\) | \(1.8321\) |
Rank
sage: E.rank()
The elliptic curves in class 299538z have rank \(1\).
Complex multiplication
The elliptic curves in class 299538z do not have complex multiplication.Modular form 299538.2.a.z
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.