Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 62422f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
62422.e1 | 62422f1 | \([1, 1, 1, -13236, -609035]\) | \(-1732323601/60416\) | \(-8943736269824\) | \([]\) | \(147840\) | \(1.2580\) | \(\Gamma_0(N)\)-optimal |
62422.e2 | 62422f2 | \([1, 1, 1, 60824, 30792405]\) | \(168105213359/2859697196\) | \(-423337816680667244\) | \([]\) | \(739200\) | \(2.0628\) |
Rank
sage: E.rank()
The elliptic curves in class 62422f have rank \(1\).
Complex multiplication
The elliptic curves in class 62422f do not have complex multiplication.Modular form 62422.2.a.f
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.