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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 30345q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30345.g2 | 30345q1 | \([1, 1, 1, 258446625, -6603697742508]\) | \(16098893047132187167/168182866341984375\) | \(-19944448982674701228403734375\) | \([2]\) | \(17233920\) | \(4.1113\) | \(\Gamma_0(N)\)-optimal |
30345.g1 | 30345q2 | \([1, 1, 1, -4093169430, -93611649792600]\) | \(63953244990201015504593/5088175635498046875\) | \(603395943857486871897216796875\) | \([2]\) | \(34467840\) | \(4.4579\) |
Rank
sage: E.rank()
The elliptic curves in class 30345q have rank \(1\).
Complex multiplication
The elliptic curves in class 30345q do not have complex multiplication.Modular form 30345.2.a.q
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.