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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 416955.cs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
416955.cs1 | 416955cs2 | \([0, -1, 1, -9671310, 218863581893]\) | \(-2126464142970105856/438611057788643355\) | \(-20634843630008638430770755\) | \([]\) | \(202500000\) | \(3.5367\) | \(\Gamma_0(N)\)-optimal* |
416955.cs2 | 416955cs1 | \([0, -1, 1, -3227460, -2612452327]\) | \(-79028701534867456/16987307596875\) | \(-799182851712977221875\) | \([]\) | \(40500000\) | \(2.7320\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 416955.cs have rank \(1\).
Complex multiplication
The elliptic curves in class 416955.cs do not have complex multiplication.Modular form 416955.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.