Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 855.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
855.a1 | 855a4 | \([1, -1, 1, -54068, 4852482]\) | \(23977812996389881/146611125\) | \(106879510125\) | \([2]\) | \(2304\) | \(1.3034\) | |
855.a2 | 855a3 | \([1, -1, 1, -11138, -363594]\) | \(209595169258201/41748046875\) | \(30434326171875\) | \([2]\) | \(2304\) | \(1.3034\) | |
855.a3 | 855a2 | \([1, -1, 1, -3443, 73482]\) | \(6189976379881/456890625\) | \(333073265625\) | \([2, 2]\) | \(1152\) | \(0.95687\) | |
855.a4 | 855a1 | \([1, -1, 1, 202, 4956]\) | \(1256216039/15582375\) | \(-11359551375\) | \([2]\) | \(576\) | \(0.61030\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 855.a have rank \(0\).
Complex multiplication
The elliptic curves in class 855.a do not have complex multiplication.Modular form 855.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.