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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 225318g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
225318.q2 | 225318g1 | \([1, 1, 1, -29912115, 67425426801]\) | \(-274585709373920209/23361765507072\) | \(-251821500866333960306688\) | \([2]\) | \(50872320\) | \(3.2351\) | \(\Gamma_0(N)\)-optimal |
225318.q1 | 225318g2 | \([1, 1, 1, -487970355, 4148724345201]\) | \(1192111508635128247249/7651496452608\) | \(82477127851741275628032\) | \([2]\) | \(101744640\) | \(3.5817\) |
Rank
sage: E.rank()
The elliptic curves in class 225318g have rank \(1\).
Complex multiplication
The elliptic curves in class 225318g do not have complex multiplication.Modular form 225318.2.a.g
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.