Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 101150a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
101150.p1 | 101150a1 | \([1, -1, 0, -18992, 956416]\) | \(9869198625/614656\) | \(47184452000000\) | \([2]\) | \(294912\) | \(1.3752\) | \(\Gamma_0(N)\)-optimal |
101150.p2 | 101150a2 | \([1, -1, 0, 15008, 3982416]\) | \(4869777375/92236816\) | \(-7080616828250000\) | \([2]\) | \(589824\) | \(1.7218\) |
Rank
sage: E.rank()
The elliptic curves in class 101150a have rank \(1\).
Complex multiplication
The elliptic curves in class 101150a do not have complex multiplication.Modular form 101150.2.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 Cremona 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 Cremona labels.