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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 2646l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2646.f2 | 2646l1 | \([1, -1, 0, -597, -7043]\) | \(-7414875/2744\) | \(-8716379112\) | \([]\) | \(1728\) | \(0.61753\) | \(\Gamma_0(N)\)-optimal |
2646.f1 | 2646l2 | \([1, -1, 0, -52047, -4557281]\) | \(-545407363875/14\) | \(-400241898\) | \([]\) | \(5184\) | \(1.1668\) | |
2646.f3 | 2646l3 | \([1, -1, 0, 4548, 71504]\) | \(4492125/3584\) | \(-8299415996928\) | \([]\) | \(5184\) | \(1.1668\) |
Rank
sage: E.rank()
The elliptic curves in class 2646l have rank \(1\).
Complex multiplication
The elliptic curves in class 2646l do not have complex multiplication.Modular form 2646.2.a.l
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.
\(\left(\begin{array}{rrr} 1 & 3 & 3 \\ 3 & 1 & 9 \\ 3 & 9 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.