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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 99275.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
99275.c1 | 99275d1 | \([0, 1, 1, -246683, -55232081]\) | \(-2258403328/480491\) | \(-353205037618296875\) | \([]\) | \(933120\) | \(2.0885\) | \(\Gamma_0(N)\)-optimal |
99275.c2 | 99275d2 | \([0, 1, 1, 1738817, 319531044]\) | \(790939860992/517504691\) | \(-380413501714496421875\) | \([]\) | \(2799360\) | \(2.6378\) |
Rank
sage: E.rank()
The elliptic curves in class 99275.c have rank \(1\).
Complex multiplication
The elliptic curves in class 99275.c do not have complex multiplication.Modular form 99275.2.a.c
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.