Show commands:
SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 40950w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
40950.e3 | 40950w1 | \([1, -1, 0, 3033, -612059]\) | \(270840023/14329224\) | \(-163218817125000\) | \([]\) | \(186624\) | \(1.4069\) | \(\Gamma_0(N)\)-optimal |
40950.e2 | 40950w2 | \([1, -1, 0, -27342, 16671316]\) | \(-198461344537/10417365504\) | \(-118660303944000000\) | \([]\) | \(559872\) | \(1.9562\) | |
40950.e1 | 40950w3 | \([1, -1, 0, -5862717, 5465375941]\) | \(-1956469094246217097/36641439744\) | \(-417368899584000000\) | \([]\) | \(1679616\) | \(2.5055\) |
Rank
sage: E.rank()
The elliptic curves in class 40950w have rank \(0\).
Complex multiplication
The elliptic curves in class 40950w do not have complex multiplication.Modular form 40950.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.