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SageMath
E = EllipticCurve("en1")
E.isogeny_class()
Elliptic curves in class 92400.en
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92400.en1 | 92400cr1 | \([0, 1, 0, -111083, -14286912]\) | \(4850878539776/130977\) | \(4093031250000\) | \([2]\) | \(332800\) | \(1.5243\) | \(\Gamma_0(N)\)-optimal |
92400.en2 | 92400cr2 | \([0, 1, 0, -106708, -15459412]\) | \(-268750151696/50014503\) | \(-25007251500000000\) | \([2]\) | \(665600\) | \(1.8709\) |
Rank
sage: E.rank()
The elliptic curves in class 92400.en have rank \(1\).
Complex multiplication
The elliptic curves in class 92400.en do not have complex multiplication.Modular form 92400.2.a.en
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.