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SageMath
E = EllipticCurve("jd1")
E.isogeny_class()
Elliptic curves in class 78400.jd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
78400.jd1 | 78400cn2 | \([0, -1, 0, -24033, 1027937]\) | \(2185454/625\) | \(439040000000000\) | \([2]\) | \(294912\) | \(1.5162\) | |
78400.jd2 | 78400cn1 | \([0, -1, 0, 3967, 103937]\) | \(19652/25\) | \(-8780800000000\) | \([2]\) | \(147456\) | \(1.1696\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 78400.jd have rank \(0\).
Complex multiplication
The elliptic curves in class 78400.jd do not have complex multiplication.Modular form 78400.2.a.jd
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.