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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 624.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
624.a1 | 624b2 | \([0, -1, 0, -60, -144]\) | \(94875856/9477\) | \(2426112\) | \([2]\) | \(192\) | \(-0.038467\) | |
624.a2 | 624b1 | \([0, -1, 0, 5, -14]\) | \(702464/4563\) | \(-73008\) | \([2]\) | \(96\) | \(-0.38504\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 624.a have rank \(1\).
Complex multiplication
The elliptic curves in class 624.a do not have complex multiplication.Modular form 624.2.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.