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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 53067.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53067.a1 | 53067d2 | \([0, -1, 1, -16138264, 24979035066]\) | \(-1713910976512/1594323\) | \(-432396566960294115963\) | \([]\) | \(3921372\) | \(2.8826\) | |
53067.a2 | 53067d1 | \([0, -1, 1, -41274, -3493414]\) | \(-28672/3\) | \(-813630425504043\) | \([]\) | \(301644\) | \(1.6001\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 53067.a have rank \(0\).
Complex multiplication
The elliptic curves in class 53067.a do not have complex multiplication.Modular form 53067.2.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.
\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.