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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 37440.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37440.n1 | 37440el1 | \([0, 0, 0, -10128, 392312]\) | \(153910165504/845\) | \(630789120\) | \([2]\) | \(36864\) | \(0.88187\) | \(\Gamma_0(N)\)-optimal |
37440.n2 | 37440el2 | \([0, 0, 0, -9948, 406928]\) | \(-9115564624/714025\) | \(-8528268902400\) | \([2]\) | \(73728\) | \(1.2284\) |
Rank
sage: E.rank()
The elliptic curves in class 37440.n have rank \(2\).
Complex multiplication
The elliptic curves in class 37440.n do not have complex multiplication.Modular form 37440.2.a.n
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.