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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 115520.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
115520.r1 | 115520cn2 | \([0, 1, 0, -420685, 78062025]\) | \(7575076864/1953125\) | \(2122945380125000000\) | \([]\) | \(2068416\) | \(2.2259\) | |
115520.r2 | 115520cn1 | \([0, 1, 0, -146325, -21585527]\) | \(318767104/125\) | \(135868504328000\) | \([]\) | \(689472\) | \(1.6766\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 115520.r have rank \(1\).
Complex multiplication
The elliptic curves in class 115520.r do not have complex multiplication.Modular form 115520.2.a.r
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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.