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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 10944.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10944.d1 | 10944bl2 | \([0, 0, 0, -40332, 3451120]\) | \(-37966934881/4952198\) | \(-946379775541248\) | \([]\) | \(57600\) | \(1.6068\) | |
10944.d2 | 10944bl1 | \([0, 0, 0, -12, -16400]\) | \(-1/608\) | \(-116190609408\) | \([]\) | \(11520\) | \(0.80209\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10944.d have rank \(1\).
Complex multiplication
The elliptic curves in class 10944.d do not have complex multiplication.Modular form 10944.2.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 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.