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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 50400.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
50400.w1 | 50400n2 | \([0, 0, 0, -1755, 25650]\) | \(474552/49\) | \(61725888000\) | \([2]\) | \(30720\) | \(0.80586\) | |
50400.w2 | 50400n1 | \([0, 0, 0, -405, -2700]\) | \(46656/7\) | \(1102248000\) | \([2]\) | \(15360\) | \(0.45929\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 50400.w have rank \(0\).
Complex multiplication
The elliptic curves in class 50400.w do not have complex multiplication.Modular form 50400.2.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.