Show commands:
SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 11310n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11310.m4 | 11310n1 | \([1, 0, 0, -28315, 523217]\) | \(2510581756496128561/1333551278592000\) | \(1333551278592000\) | \([4]\) | \(69120\) | \(1.5936\) | \(\Gamma_0(N)\)-optimal |
11310.m2 | 11310n2 | \([1, 0, 0, -261595, -51124975]\) | \(1979758117698975186481/17510434929000000\) | \(17510434929000000\) | \([2, 2]\) | \(138240\) | \(1.9402\) | |
11310.m1 | 11310n3 | \([1, 0, 0, -4176595, -3285697975]\) | \(8057323694463985606146481/638717154543000\) | \(638717154543000\) | \([2]\) | \(276480\) | \(2.2868\) | |
11310.m3 | 11310n4 | \([1, 0, 0, -79075, -121103143]\) | \(-54681655838565466801/6303365630859375000\) | \(-6303365630859375000\) | \([2]\) | \(276480\) | \(2.2868\) |
Rank
sage: E.rank()
The elliptic curves in class 11310n have rank \(1\).
Complex multiplication
The elliptic curves in class 11310n do not have complex multiplication.Modular form 11310.2.a.n
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.