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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 37180.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37180.a1 | 37180d4 | \([0, 1, 0, -1199956, -506336700]\) | \(154639330142416/33275\) | \(41116689785600\) | \([2]\) | \(466560\) | \(1.9969\) | |
37180.a2 | 37180d3 | \([0, 1, 0, -75261, -7871876]\) | \(610462990336/8857805\) | \(684078926307920\) | \([2]\) | \(233280\) | \(1.6504\) | |
37180.a3 | 37180d2 | \([0, 1, 0, -16956, -485900]\) | \(436334416/171875\) | \(212379596000000\) | \([2]\) | \(155520\) | \(1.4476\) | |
37180.a4 | 37180d1 | \([0, 1, 0, -7661, 250264]\) | \(643956736/15125\) | \(1168087778000\) | \([2]\) | \(77760\) | \(1.1010\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 37180.a have rank \(1\).
Complex multiplication
The elliptic curves in class 37180.a do not have complex multiplication.Modular form 37180.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.