Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 1150d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1150.a2 | 1150d1 | \([1, 0, 1, -951, -9202]\) | \(243135625/48668\) | \(19010937500\) | \([3]\) | \(720\) | \(0.68845\) | \(\Gamma_0(N)\)-optimal |
1150.a1 | 1150d2 | \([1, 0, 1, -72826, -7570452]\) | \(109348914285625/1472\) | \(575000000\) | \([]\) | \(2160\) | \(1.2378\) |
Rank
sage: E.rank()
The elliptic curves in class 1150d have rank \(1\).
Complex multiplication
The elliptic curves in class 1150d do not have complex multiplication.Modular form 1150.2.a.d
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.