Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 53816.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53816.a1 | 53816a2 | \([0, 1, 0, -38760, 2888944]\) | \(3543122/49\) | \(89062769395712\) | \([2]\) | \(241920\) | \(1.4823\) | |
53816.a2 | 53816a1 | \([0, 1, 0, -320, 121264]\) | \(-4/7\) | \(-6361626385408\) | \([2]\) | \(120960\) | \(1.1358\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 53816.a have rank \(1\).
Complex multiplication
The elliptic curves in class 53816.a do not have complex multiplication.Modular form 53816.2.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.