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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 30400.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30400.h1 | 30400y2 | \([0, 1, 0, -38513, 2896303]\) | \(3084800518928/361\) | \(739328000\) | \([2]\) | \(57344\) | \(1.1237\) | |
30400.h2 | 30400y1 | \([0, 1, 0, -2413, 44403]\) | \(12144109568/130321\) | \(16681088000\) | \([2]\) | \(28672\) | \(0.77709\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 30400.h have rank \(1\).
Complex multiplication
The elliptic curves in class 30400.h do not have complex multiplication.Modular form 30400.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.