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SageMath
E = EllipticCurve("dv1")
E.isogeny_class()
Elliptic curves in class 265650.dv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
265650.dv1 | 265650dv3 | \([1, 0, 1, -239646551, 1427901569498]\) | \(97413070452067229637409633/140666577176907936\) | \(2197915268389186500000\) | \([2]\) | \(47185920\) | \(3.3658\) | |
265650.dv2 | 265650dv4 | \([1, 0, 1, -38390551, -61771758502]\) | \(400476194988122984445793/126270124548858769248\) | \(1972970696075918269500000\) | \([2]\) | \(47185920\) | \(3.3658\) | |
265650.dv3 | 265650dv2 | \([1, 0, 1, -15114551, 21882185498]\) | \(24439335640029940889953/902916953746891776\) | \(14108077402295184000000\) | \([2, 2]\) | \(23592960\) | \(3.0193\) | |
265650.dv4 | 265650dv1 | \([1, 0, 1, 373449, 1221193498]\) | \(368637286278891167/41443067603976192\) | \(-647547931312128000000\) | \([2]\) | \(11796480\) | \(2.6727\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 265650.dv have rank \(1\).
Complex multiplication
The elliptic curves in class 265650.dv do not have complex multiplication.Modular form 265650.2.a.dv
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.