Show commands:
SageMath
E = EllipticCurve("oh1")
E.isogeny_class()
Elliptic curves in class 381150.oh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
381150.oh1 | 381150oh2 | \([1, -1, 1, -9542930, -12003000303]\) | \(-7620530425/526848\) | \(-6644602700505000000000\) | \([]\) | \(27993600\) | \(2.9383\) | |
381150.oh2 | 381150oh1 | \([1, -1, 1, 666445, -17194053]\) | \(2595575/1512\) | \(-19069331729765625000\) | \([]\) | \(9331200\) | \(2.3890\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 381150.oh have rank \(1\).
Complex multiplication
The elliptic curves in class 381150.oh do not have complex multiplication.Modular form 381150.2.a.oh
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.