Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 441.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
441.a1 | 441f2 | \([0, 0, 1, -8211, -286610]\) | \(-1713910976512/1594323\) | \(-56950811883\) | \([]\) | \(624\) | \(0.98669\) | |
441.a2 | 441f1 | \([0, 0, 1, -21, 40]\) | \(-28672/3\) | \(-107163\) | \([]\) | \(48\) | \(-0.29578\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 441.a have rank \(1\).
Complex multiplication
The elliptic curves in class 441.a do not have complex multiplication.Modular form 441.2.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.
\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.