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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 3360.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3360.s1 | 3360t3 | \([0, 1, 0, -376, 2684]\) | \(11512557512/2835\) | \(1451520\) | \([2]\) | \(1024\) | \(0.17027\) | |
3360.s2 | 3360t2 | \([0, 1, 0, -176, -936]\) | \(1184287112/36015\) | \(18439680\) | \([2]\) | \(1024\) | \(0.17027\) | |
3360.s3 | 3360t1 | \([0, 1, 0, -26, 24]\) | \(31554496/11025\) | \(705600\) | \([2, 2]\) | \(512\) | \(-0.17631\) | \(\Gamma_0(N)\)-optimal |
3360.s4 | 3360t4 | \([0, 1, 0, 79, 255]\) | \(13144256/13125\) | \(-53760000\) | \([2]\) | \(1024\) | \(0.17027\) |
Rank
sage: E.rank()
The elliptic curves in class 3360.s have rank \(0\).
Complex multiplication
The elliptic curves in class 3360.s do not have complex multiplication.Modular form 3360.2.a.s
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.