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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 35574.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35574.h1 | 35574j4 | \([1, 1, 0, -83794680, -295252549038]\) | \(312196988566716625/25367712678\) | \(5287199053762660068342\) | \([2]\) | \(3317760\) | \(3.2135\) | |
35574.h2 | 35574j3 | \([1, 1, 0, -4879690, -5271526784]\) | \(-61653281712625/21875235228\) | \(-4559288591226498575292\) | \([2]\) | \(1658880\) | \(2.8669\) | |
35574.h3 | 35574j2 | \([1, 1, 0, -2152350, 608689404]\) | \(5290763640625/2291573592\) | \(477615222193739009688\) | \([2]\) | \(1105920\) | \(2.6642\) | |
35574.h4 | 35574j1 | \([1, 1, 0, 456410, 70763092]\) | \(50447927375/39517632\) | \(-8236358916921229248\) | \([2]\) | \(552960\) | \(2.3176\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 35574.h have rank \(1\).
Complex multiplication
The elliptic curves in class 35574.h do not have complex multiplication.Modular form 35574.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.