Show commands:
SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 7938ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7938.s2 | 7938ba1 | \([1, -1, 1, 211, -171]\) | \(109503/64\) | \(-609892416\) | \([]\) | \(3456\) | \(0.37515\) | \(\Gamma_0(N)\)-optimal |
| 7938.s1 | 7938ba2 | \([1, -1, 1, -2729, 60589]\) | \(-35937/4\) | \(-250094008836\) | \([]\) | \(10368\) | \(0.92445\) |
Rank
sage: E.rank()
The elliptic curves in class 7938ba have rank \(1\).
Complex multiplication
The elliptic curves in class 7938ba do not have complex multiplication.Modular form 7938.2.a.ba
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.
