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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 74360.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 74360.l1 | 74360s1 | \([0, 0, 0, -6422, -191139]\) | \(379275264/15125\) | \(1168087778000\) | \([2]\) | \(112896\) | \(1.0820\) | \(\Gamma_0(N)\)-optimal |
| 74360.l2 | 74360s2 | \([0, 0, 0, 2873, -698646]\) | \(2122416/171875\) | \(-212379596000000\) | \([2]\) | \(225792\) | \(1.4286\) |
Rank
sage: E.rank()
The elliptic curves in class 74360.l have rank \(0\).
Complex multiplication
The elliptic curves in class 74360.l do not have complex multiplication.Modular form 74360.2.a.l
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.
