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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 73034d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
73034.h2 | 73034d1 | \([1, -1, 0, -7549, 388037]\) | \(-2146689/1664\) | \(-36881496918656\) | \([]\) | \(288288\) | \(1.3020\) | \(\Gamma_0(N)\)-optimal |
73034.h1 | 73034d2 | \([1, -1, 0, -597439, -194865553]\) | \(-1064019559329/125497034\) | \(-2781561582194391386\) | \([]\) | \(2018016\) | \(2.2749\) |
Rank
sage: E.rank()
The elliptic curves in class 73034d have rank \(1\).
Complex multiplication
The elliptic curves in class 73034d do not have complex multiplication.Modular form 73034.2.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.