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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 37905e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37905.j3 | 37905e1 | \([0, -1, 1, 17569, -794578]\) | \(12747309056/13089195\) | \(-615792710355795\) | \([]\) | \(129600\) | \(1.5246\) | \(\Gamma_0(N)\)-optimal |
| 37905.j2 | 37905e2 | \([0, -1, 1, -177371, 41185751]\) | \(-13117540040704/7940149875\) | \(-373551346141414875\) | \([]\) | \(388800\) | \(2.0740\) | |
| 37905.j1 | 37905e3 | \([0, -1, 1, -16021661, 24688995392]\) | \(-9667735243366334464/779296875\) | \(-36662708044921875\) | \([]\) | \(1166400\) | \(2.6233\) |
Rank
sage: E.rank()
The elliptic curves in class 37905e have rank \(1\).
Complex multiplication
The elliptic curves in class 37905e do not have complex multiplication.Modular form 37905.2.a.e
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 Cremona numbering.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
