Show commands:
SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 54080.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54080.i1 | 54080s2 | \([0, 1, 0, -4281, -108185]\) | \(438976/5\) | \(98853048320\) | \([2]\) | \(61440\) | \(0.92300\) | |
54080.i2 | 54080s1 | \([0, 1, 0, -56, -4250]\) | \(-64/25\) | \(-7722894400\) | \([2]\) | \(30720\) | \(0.57643\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 54080.i have rank \(1\).
Complex multiplication
The elliptic curves in class 54080.i do not have complex multiplication.Modular form 54080.2.a.i
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.