Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 1320.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1320.a1 | 1320e1 | \([0, -1, 0, -10931, -436260]\) | \(9028656748079104/3969405\) | \(63510480\) | \([2]\) | \(1536\) | \(0.83864\) | \(\Gamma_0(N)\)-optimal |
1320.a2 | 1320e2 | \([0, -1, 0, -10876, -440924]\) | \(-555816294307024/11837848275\) | \(-3030489158400\) | \([2]\) | \(3072\) | \(1.1852\) |
Rank
sage: E.rank()
The elliptic curves in class 1320.a have rank \(0\).
Complex multiplication
The elliptic curves in class 1320.a do not have complex multiplication.Modular form 1320.2.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.