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SageMath
E = EllipticCurve("jp1")
E.isogeny_class()
Elliptic curves in class 176400jp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 176400.ec1 | 176400jp1 | \([0, 0, 0, -37275, 2770250]\) | \(-67645179/8\) | \(-677376000000\) | \([]\) | \(373248\) | \(1.2956\) | \(\Gamma_0(N)\)-optimal |
| 176400.ec2 | 176400jp2 | \([0, 0, 0, 4725, 8552250]\) | \(189/512\) | \(-31603654656000000\) | \([]\) | \(1119744\) | \(1.8450\) |
Rank
sage: E.rank()
The elliptic curves in class 176400jp have rank \(1\).
Complex multiplication
The elliptic curves in class 176400jp do not have complex multiplication.Modular form 176400.2.a.jp
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
