Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 29645.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
29645.a1 | 29645b2 | \([1, -1, 1, -3268, 69556]\) | \(24642171/1225\) | \(191823753275\) | \([2]\) | \(27648\) | \(0.92394\) | |
29645.a2 | 29645b1 | \([1, -1, 1, -573, -3748]\) | \(132651/35\) | \(5480678665\) | \([2]\) | \(13824\) | \(0.57736\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 29645.a have rank \(2\).
Complex multiplication
The elliptic curves in class 29645.a do not have complex multiplication.Modular form 29645.2.a.a
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.