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SageMath
E = EllipticCurve("dd1")
E.isogeny_class()
Elliptic curves in class 281554.dd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
281554.dd1 | 281554dd2 | \([1, -1, 1, -67801, -2973785]\) | \(60698457/28322\) | \(16083192956305202\) | \([2]\) | \(1806336\) | \(1.8042\) | |
281554.dd2 | 281554dd1 | \([1, -1, 1, 15009, -356989]\) | \(658503/476\) | \(-270305763971516\) | \([2]\) | \(903168\) | \(1.4576\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 281554.dd have rank \(0\).
Complex multiplication
The elliptic curves in class 281554.dd do not have complex multiplication.Modular form 281554.2.a.dd
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.