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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 190440.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
190440.n1 | 190440bk3 | \([0, 0, 0, -5029203, 4271906702]\) | \(63649751618/1164375\) | \(257345968409475840000\) | \([2]\) | \(6488064\) | \(2.7113\) | |
190440.n2 | 190440bk2 | \([0, 0, 0, -649083, -100329082]\) | \(273671716/119025\) | \(13153238385373209600\) | \([2, 2]\) | \(3244032\) | \(2.3647\) | |
190440.n3 | 190440bk1 | \([0, 0, 0, -553863, -158584678]\) | \(680136784/345\) | \(9531332163313920\) | \([2]\) | \(1622016\) | \(2.0181\) | \(\Gamma_0(N)\)-optimal |
190440.n4 | 190440bk4 | \([0, 0, 0, 2207517, -744206722]\) | \(5382838942/4197615\) | \(-927741747448323717120\) | \([2]\) | \(6488064\) | \(2.7113\) |
Rank
sage: E.rank()
The elliptic curves in class 190440.n have rank \(1\).
Complex multiplication
The elliptic curves in class 190440.n do not have complex multiplication.Modular form 190440.2.a.n
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.