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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 195994h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
195994.b2 | 195994h1 | \([1, 1, 0, -523305, 184827781]\) | \(-2507141976625/889192448\) | \(-5620908284237053952\) | \([]\) | \(3701376\) | \(2.3087\) | \(\Gamma_0(N)\)-optimal |
195994.b1 | 195994h2 | \([1, 1, 0, -45490985, 118077304453]\) | \(-1646982616152408625/38112512\) | \(-240923025061369088\) | \([]\) | \(11104128\) | \(2.8580\) |
Rank
sage: E.rank()
The elliptic curves in class 195994h have rank \(0\).
Complex multiplication
The elliptic curves in class 195994h do not have complex multiplication.Modular form 195994.2.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 Cremona 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 Cremona labels.