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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 2925.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2925.k1 | 2925a2 | \([0, 0, 1, -9450, -355219]\) | \(-303464448/1625\) | \(-499763671875\) | \([]\) | \(3456\) | \(1.0893\) | |
2925.k2 | 2925a1 | \([0, 0, 1, 300, -2594]\) | \(7077888/10985\) | \(-4634296875\) | \([]\) | \(1152\) | \(0.54000\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2925.k have rank \(1\).
Complex multiplication
The elliptic curves in class 2925.k do not have complex multiplication.Modular form 2925.2.a.k
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.