Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 8820.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8820.a1 | 8820r1 | \([0, 0, 0, -439383, 112169918]\) | \(-177953104/125\) | \(-6589582608672000\) | \([]\) | \(90720\) | \(1.9716\) | \(\Gamma_0(N)\)-optimal |
8820.a2 | 8820r2 | \([0, 0, 0, 424977, 476411222]\) | \(161017136/1953125\) | \(-102962228260500000000\) | \([]\) | \(272160\) | \(2.5210\) |
Rank
sage: E.rank()
The elliptic curves in class 8820.a have rank \(0\).
Complex multiplication
The elliptic curves in class 8820.a do not have complex multiplication.Modular form 8820.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.