Show commands:
SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 2880w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2880.w2 | 2880w1 | \([0, 0, 0, -12, 144]\) | \(-108/5\) | \(-8847360\) | \([2]\) | \(512\) | \(0.012990\) | \(\Gamma_0(N)\)-optimal |
2880.w1 | 2880w2 | \([0, 0, 0, -492, 4176]\) | \(3721734/25\) | \(88473600\) | \([2]\) | \(1024\) | \(0.35956\) |
Rank
sage: E.rank()
The elliptic curves in class 2880w have rank \(1\).
Complex multiplication
The elliptic curves in class 2880w do not have complex multiplication.Modular form 2880.2.a.w
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.