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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 407330e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
407330.e1 | 407330e1 | \([1, 0, 1, -218753, 95240748]\) | \(-14782919881/41503000\) | \(-3250140822117343000\) | \([3]\) | \(8584704\) | \(2.2393\) | \(\Gamma_0(N)\)-optimal |
407330.e2 | 407330e2 | \([1, 0, 1, 1910472, -2172809722]\) | \(9847440872519/31746373120\) | \(-2486089758125454046720\) | \([]\) | \(25754112\) | \(2.7886\) |
Rank
sage: E.rank()
The elliptic curves in class 407330e have rank \(0\).
Complex multiplication
The elliptic curves in class 407330e do not have complex multiplication.Modular form 407330.2.a.e
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.