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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 64400a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
64400.bf2 | 64400a1 | \([0, 0, 0, -1475, -24750]\) | \(-22180932/3703\) | \(-59248000000\) | \([2]\) | \(32768\) | \(0.79409\) | \(\Gamma_0(N)\)-optimal |
64400.bf1 | 64400a2 | \([0, 0, 0, -24475, -1473750]\) | \(50668941906/1127\) | \(36064000000\) | \([2]\) | \(65536\) | \(1.1407\) |
Rank
sage: E.rank()
The elliptic curves in class 64400a have rank \(1\).
Complex multiplication
The elliptic curves in class 64400a do not have complex multiplication.Modular form 64400.2.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 Cremona 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 Cremona labels.