Show commands:
SageMath
E = EllipticCurve("fu1")
E.isogeny_class()
Elliptic curves in class 308550.fu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
308550.fu1 | 308550fu1 | \([1, 1, 1, -592963, 175389281]\) | \(832972004929/610368\) | \(16895377257000000\) | \([2]\) | \(3686400\) | \(2.0480\) | \(\Gamma_0(N)\)-optimal |
308550.fu2 | 308550fu2 | \([1, 1, 1, -471963, 249199281]\) | \(-420021471169/727634952\) | \(-20141401612501125000\) | \([2]\) | \(7372800\) | \(2.3946\) |
Rank
sage: E.rank()
The elliptic curves in class 308550.fu have rank \(1\).
Complex multiplication
The elliptic curves in class 308550.fu do not have complex multiplication.Modular form 308550.2.a.fu
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.