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SageMath
E = EllipticCurve("lm1")
E.isogeny_class()
Elliptic curves in class 366912.lm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 366912.lm1 | 366912lm2 | \([0, 0, 0, -103708975692, -12855016276940432]\) | \(-5486773802537974663600129/2635437714\) | \(-59252741207985329012736\) | \([]\) | \(606928896\) | \(4.6085\) | |
| 366912.lm2 | 366912lm1 | \([0, 0, 0, 20151348, -393401347472]\) | \(40251338884511/2997011332224\) | \(-67382027631432770022014976\) | \([]\) | \(86704128\) | \(3.6356\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 366912.lm have rank \(1\).
Complex multiplication
The elliptic curves in class 366912.lm do not have complex multiplication.Modular form 366912.2.a.lm
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
