Show commands:
SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 9576.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9576.t1 | 9576v3 | \([0, 0, 0, -5335419, -4743521242]\) | \(22501000029889239268/3620708343\) | \(2702844295216128\) | \([2]\) | \(196608\) | \(2.3635\) | |
9576.t2 | 9576v2 | \([0, 0, 0, -334479, -73643470]\) | \(22174957026242512/278654127129\) | \(52003547821322496\) | \([2, 2]\) | \(98304\) | \(2.0169\) | |
9576.t3 | 9576v4 | \([0, 0, 0, -57459, -191931010]\) | \(-28104147578308/21301741002339\) | \(-15901664451282054144\) | \([2]\) | \(196608\) | \(2.3635\) | |
9576.t4 | 9576v1 | \([0, 0, 0, -39234, 1171613]\) | \(572616640141312/280535480757\) | \(3272165847549648\) | \([2]\) | \(49152\) | \(1.6703\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9576.t have rank \(0\).
Complex multiplication
The elliptic curves in class 9576.t do not have complex multiplication.Modular form 9576.2.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.