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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 6160.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6160.a1 | 6160h2 | \([0, 1, 0, -1176, 15124]\) | \(43949604889/42350\) | \(173465600\) | \([2]\) | \(3072\) | \(0.50213\) | |
6160.a2 | 6160h1 | \([0, 1, 0, -56, 340]\) | \(-4826809/10780\) | \(-44154880\) | \([2]\) | \(1536\) | \(0.15556\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6160.a have rank \(1\).
Complex multiplication
The elliptic curves in class 6160.a do not have complex multiplication.Modular form 6160.2.a.a
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.