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SageMath
E = EllipticCurve("gj1")
E.isogeny_class()
Elliptic curves in class 270400.gj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
270400.gj1 | 270400gj2 | \([0, 1, 0, -901333, 328130713]\) | \(671088640/2197\) | \(265112484325000000\) | \([]\) | \(4354560\) | \(2.2086\) | |
270400.gj2 | 270400gj1 | \([0, 1, 0, -56333, -4799287]\) | \(163840/13\) | \(1568712925000000\) | \([]\) | \(1451520\) | \(1.6593\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 270400.gj have rank \(1\).
Complex multiplication
The elliptic curves in class 270400.gj do not have complex multiplication.Modular form 270400.2.a.gj
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.