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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 331200.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 331200.be1 | 331200be4 | \([0, 0, 0, -120552300, 508685778000]\) | \(2403250125069123/4232000000\) | \(341190475776000000000000\) | \([2]\) | \(47775744\) | \(3.4087\) | |
| 331200.be2 | 331200be3 | \([0, 0, 0, -9960300, 2395602000]\) | \(1355469437763/753664000\) | \(60761573425152000000000\) | \([2]\) | \(23887872\) | \(3.0621\) | |
| 331200.be3 | 331200be2 | \([0, 0, 0, -6288300, -5409118000]\) | \(248656466619387/29607177800\) | \(3274317007257600000000\) | \([2]\) | \(15925248\) | \(2.8594\) | |
| 331200.be4 | 331200be1 | \([0, 0, 0, -6096300, -5793502000]\) | \(226568219476347/3893440\) | \(430583316480000000\) | \([2]\) | \(7962624\) | \(2.5128\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 331200.be have rank \(1\).
Complex multiplication
The elliptic curves in class 331200.be do not have complex multiplication.Modular form 331200.2.a.be
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.
