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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 15030d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15030.b2 | 15030d1 | \([1, -1, 0, -13320, -2548800]\) | \(-358531401121921/3652290000000\) | \(-2662519410000000\) | \([]\) | \(75264\) | \(1.6420\) | \(\Gamma_0(N)\)-optimal |
15030.b1 | 15030d2 | \([1, -1, 0, -3424770, 2477628270]\) | \(-6093832136609347161121/108676727597808690\) | \(-79225334418802535010\) | \([]\) | \(526848\) | \(2.6150\) |
Rank
sage: E.rank()
The elliptic curves in class 15030d have rank \(1\).
Complex multiplication
The elliptic curves in class 15030d do not have complex multiplication.Modular form 15030.2.a.d
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.