Show commands:
SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 10626e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10626.g1 | 10626e1 | \([1, 0, 1, -8401, 295652]\) | \(-65560514292015625/149954112\) | \(-149954112\) | \([3]\) | \(14688\) | \(0.81262\) | \(\Gamma_0(N)\)-optimal |
10626.g2 | 10626e2 | \([1, 0, 1, -5776, 484190]\) | \(-21305767155765625/89149883547648\) | \(-89149883547648\) | \([]\) | \(44064\) | \(1.3619\) |
Rank
sage: E.rank()
The elliptic curves in class 10626e have rank \(1\).
Complex multiplication
The elliptic curves in class 10626e do not have complex multiplication.Modular form 10626.2.a.e
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.