Show commands:
SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 191634n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
191634.g1 | 191634n1 | \([1, 0, 1, -168812, 2864810]\) | \(7719308351835137/4415243157504\) | \(304302973658333184\) | \([2]\) | \(2856960\) | \(2.0445\) | \(\Gamma_0(N)\)-optimal |
191634.g2 | 191634n2 | \([1, 0, 1, 670868, 23017130]\) | \(484489425895814143/283680450809856\) | \(-19551540350266085376\) | \([2]\) | \(5713920\) | \(2.3910\) |
Rank
sage: E.rank()
The elliptic curves in class 191634n have rank \(0\).
Complex multiplication
The elliptic curves in class 191634n do not have complex multiplication.Modular form 191634.2.a.n
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.