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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 30400.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30400.w1 | 30400cb2 | \([0, 0, 0, -1580, -23600]\) | \(13312053/361\) | \(11829248000\) | \([2]\) | \(16384\) | \(0.71306\) | |
30400.w2 | 30400cb1 | \([0, 0, 0, 20, -1200]\) | \(27/19\) | \(-622592000\) | \([2]\) | \(8192\) | \(0.36649\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 30400.w have rank \(0\).
Complex multiplication
The elliptic curves in class 30400.w do not have complex multiplication.Modular form 30400.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.