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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 294438.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
294438.h1 | 294438h2 | \([1, 0, 0, -501386934491, -136649411373708603]\) | \(13939357289517572926833783386157182185009/83397273661420954726097196\) | \(83397273661420954726097196\) | \([]\) | \(1005884544\) | \(5.0396\) | |
294438.h2 | 294438h1 | \([1, 0, 0, -714643631, 6065661961017]\) | \(40363823168204992312149665459569/7464127685965932538179403776\) | \(7464127685965932538179403776\) | \([7]\) | \(143697792\) | \(4.0666\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 294438.h have rank \(1\).
Complex multiplication
The elliptic curves in class 294438.h do not have complex multiplication.Modular form 294438.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.