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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 83655t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 83655.bb4 | 83655t1 | \([1, -1, 0, 1236, -13285]\) | \(59319/55\) | \(-193530906855\) | \([2]\) | \(73728\) | \(0.85297\) | \(\Gamma_0(N)\)-optimal |
| 83655.bb3 | 83655t2 | \([1, -1, 0, -6369, -115192]\) | \(8120601/3025\) | \(10644199877025\) | \([2, 2]\) | \(147456\) | \(1.1995\) | |
| 83655.bb2 | 83655t3 | \([1, -1, 0, -44394, 3527603]\) | \(2749884201/73205\) | \(257589637024005\) | \([2]\) | \(294912\) | \(1.5461\) | |
| 83655.bb1 | 83655t4 | \([1, -1, 0, -90024, -10371295]\) | \(22930509321/6875\) | \(24191363356875\) | \([2]\) | \(294912\) | \(1.5461\) |
Rank
sage: E.rank()
The elliptic curves in class 83655t have rank \(1\).
Complex multiplication
The elliptic curves in class 83655t do not have complex multiplication.Modular form 83655.2.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 Cremona 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 Cremona labels.
