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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 30345.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30345.t1 | 30345b4 | \([1, 1, 0, -32518, -2270453]\) | \(157551496201/13125\) | \(316805593125\) | \([2]\) | \(81920\) | \(1.2506\) | |
30345.t2 | 30345b2 | \([1, 1, 0, -2173, -30992]\) | \(47045881/11025\) | \(266116698225\) | \([2, 2]\) | \(40960\) | \(0.90407\) | |
30345.t3 | 30345b1 | \([1, 1, 0, -728, 6867]\) | \(1771561/105\) | \(2534444745\) | \([2]\) | \(20480\) | \(0.55750\) | \(\Gamma_0(N)\)-optimal |
30345.t4 | 30345b3 | \([1, 1, 0, 5052, -185607]\) | \(590589719/972405\) | \(-23471492783445\) | \([2]\) | \(81920\) | \(1.2506\) |
Rank
sage: E.rank()
The elliptic curves in class 30345.t have rank \(1\).
Complex multiplication
The elliptic curves in class 30345.t do not have complex multiplication.Modular form 30345.2.a.t
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.