Show commands:
SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 370881w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality | CM discriminant |
---|---|---|---|---|---|---|---|---|---|
370881.w2 | 370881w1 | \([0, 0, 1, 0, 424545420]\) | \(0\) | \(-77863167585467615547\) | \([3]\) | \(7454160\) | \(2.4957\) | \(\Gamma_0(N)\)-optimal | \(-3\) |
370881.w1 | 370881w2 | \([0, 0, 1, 0, -11462726347]\) | \(0\) | \(-56762249169805891733763\) | \([]\) | \(22362480\) | \(3.0450\) | \(-3\) |
Rank
sage: E.rank()
The elliptic curves in class 370881w have rank \(0\).
Complex multiplication
Each elliptic curve in class 370881w has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).Modular form 370881.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.