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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 119025.co
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
119025.co1 | 119025bs2 | \([0, 0, 1, -991875, -389724219]\) | \(-102400/3\) | \(-3161664934013671875\) | \([]\) | \(2851200\) | \(2.3287\) | |
119025.co2 | 119025bs1 | \([0, 0, 1, 7935, 1201491]\) | \(20480/243\) | \(-655602840717075\) | \([]\) | \(570240\) | \(1.5240\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 119025.co have rank \(1\).
Complex multiplication
The elliptic curves in class 119025.co do not have complex multiplication.Modular form 119025.2.a.co
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.