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SageMath
E = EllipticCurve("cl1")
E.isogeny_class()
Elliptic curves in class 157170.cl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
157170.cl1 | 157170q2 | \([1, 0, 0, -36917631, 86334300441]\) | \(1152829477932246539641/3188367360\) | \(15389640268554240\) | \([2]\) | \(9584640\) | \(2.7642\) | |
157170.cl2 | 157170q1 | \([1, 0, 0, -2306431, 1349959961]\) | \(-281115640967896441/468084326400\) | \(-2259353639426457600\) | \([2]\) | \(4792320\) | \(2.4176\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 157170.cl have rank \(1\).
Complex multiplication
The elliptic curves in class 157170.cl do not have complex multiplication.Modular form 157170.2.a.cl
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.