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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 303450.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
303450.a1 | 303450a2 | \([1, 1, 0, -101300, -13172400]\) | \(-7620530425/526848\) | \(-7948018720320000\) | \([]\) | \(3265920\) | \(1.8019\) | |
303450.a2 | 303450a1 | \([1, 1, 0, 7075, -15675]\) | \(2595575/1512\) | \(-22810002705000\) | \([]\) | \(1088640\) | \(1.2526\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 303450.a have rank \(0\).
Complex multiplication
The elliptic curves in class 303450.a do not have complex multiplication.Modular form 303450.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.