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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 40362h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
40362.b2 | 40362h1 | \([1, 1, 0, -13171966, -20561649500]\) | \(-9559173016567/1372257936\) | \(-36281981334822246835056\) | \([2]\) | \(3999744\) | \(3.0595\) | \(\Gamma_0(N)\)-optimal |
40362.b1 | 40362h2 | \([1, 1, 0, -217538226, -1235028586176]\) | \(43060118286713527/729137052\) | \(19278108158225523281892\) | \([2]\) | \(7999488\) | \(3.4061\) |
Rank
sage: E.rank()
The elliptic curves in class 40362h have rank \(1\).
Complex multiplication
The elliptic curves in class 40362h do not have complex multiplication.Modular form 40362.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.