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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 142956.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
142956.h1 | 142956f2 | \([0, 0, 0, -7239, -236626]\) | \(622708432/1331\) | \(89671152384\) | \([]\) | \(217728\) | \(0.98598\) | |
142956.h2 | 142956f1 | \([0, 0, 0, -399, 2774]\) | \(104272/11\) | \(741083904\) | \([]\) | \(72576\) | \(0.43668\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 142956.h have rank \(1\).
Complex multiplication
The elliptic curves in class 142956.h do not have complex multiplication.Modular form 142956.2.a.h
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.