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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 29095.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
29095.d1 | 29095a4 | \([1, -1, 0, -31310, -2124059]\) | \(22930509321/6875\) | \(1017746736875\) | \([2]\) | \(49280\) | \(1.2821\) | |
29095.d2 | 29095a3 | \([1, -1, 0, -15440, 725135]\) | \(2749884201/73205\) | \(10836967254245\) | \([2]\) | \(49280\) | \(1.2821\) | |
29095.d3 | 29095a2 | \([1, -1, 0, -2215, -23400]\) | \(8120601/3025\) | \(447808564225\) | \([2, 2]\) | \(24640\) | \(0.93551\) | |
29095.d4 | 29095a1 | \([1, -1, 0, 430, -2769]\) | \(59319/55\) | \(-8141973895\) | \([2]\) | \(12320\) | \(0.58893\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 29095.d have rank \(1\).
Complex multiplication
The elliptic curves in class 29095.d do not have complex multiplication.Modular form 29095.2.a.d
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.