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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 3696.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3696.t1 | 3696w5 | \([0, 1, 0, -72304, 7459220]\) | \(10206027697760497/5557167\) | \(22762156032\) | \([4]\) | \(10240\) | \(1.3159\) | |
| 3696.t2 | 3696w3 | \([0, 1, 0, -4544, 114036]\) | \(2533811507137/58110129\) | \(238019088384\) | \([2, 4]\) | \(5120\) | \(0.96936\) | |
| 3696.t3 | 3696w2 | \([0, 1, 0, -624, -3564]\) | \(6570725617/2614689\) | \(10709766144\) | \([2, 2]\) | \(2560\) | \(0.62279\) | |
| 3696.t4 | 3696w1 | \([0, 1, 0, -544, -5068]\) | \(4354703137/1617\) | \(6623232\) | \([2]\) | \(1280\) | \(0.27622\) | \(\Gamma_0(N)\)-optimal |
| 3696.t5 | 3696w6 | \([0, 1, 0, 496, 357972]\) | \(3288008303/13504609503\) | \(-55314880524288\) | \([4]\) | \(10240\) | \(1.3159\) | |
| 3696.t6 | 3696w4 | \([0, 1, 0, 2016, -23628]\) | \(221115865823/190238433\) | \(-779216621568\) | \([2]\) | \(5120\) | \(0.96936\) |
Rank
sage: E.rank()
The elliptic curves in class 3696.t have rank \(0\).
Complex multiplication
The elliptic curves in class 3696.t do not have complex multiplication.Modular form 3696.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 8 & 4 & 2 & 1 & 8 & 4 \\ 4 & 2 & 4 & 8 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
