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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 41280cs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 41280.w3 | 41280cs1 | \([0, -1, 0, -2580, -49590]\) | \(29687332481344/1935\) | \(123840\) | \([2]\) | \(18432\) | \(0.43526\) | \(\Gamma_0(N)\)-optimal |
| 41280.w2 | 41280cs2 | \([0, -1, 0, -2585, -49383]\) | \(466566337216/3744225\) | \(15336345600\) | \([2, 2]\) | \(36864\) | \(0.78184\) | |
| 41280.w4 | 41280cs3 | \([0, -1, 0, -865, -115775]\) | \(-2186875592/176326875\) | \(-5777879040000\) | \([2]\) | \(73728\) | \(1.1284\) | |
| 41280.w1 | 41280cs4 | \([0, -1, 0, -4385, 30177]\) | \(284630612552/153846045\) | \(5041227202560\) | \([4]\) | \(73728\) | \(1.1284\) |
Rank
sage: E.rank()
The elliptic curves in class 41280cs have rank \(0\).
Complex multiplication
The elliptic curves in class 41280cs do not have complex multiplication.Modular form 41280.2.a.cs
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
