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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 5915f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5915.f2 | 5915f1 | \([0, 1, 1, -225, 1369]\) | \(-262144/35\) | \(-168938315\) | \([]\) | \(1368\) | \(0.31132\) | \(\Gamma_0(N)\)-optimal |
5915.f3 | 5915f2 | \([0, 1, 1, 1465, -3194]\) | \(71991296/42875\) | \(-206949435875\) | \([]\) | \(4104\) | \(0.86063\) | |
5915.f1 | 5915f3 | \([0, 1, 1, -22195, -1338801]\) | \(-250523582464/13671875\) | \(-65991529296875\) | \([]\) | \(12312\) | \(1.4099\) |
Rank
sage: E.rank()
The elliptic curves in class 5915f have rank \(0\).
Complex multiplication
The elliptic curves in class 5915f do not have complex multiplication.Modular form 5915.2.a.f
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.