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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 374790b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
374790.b1 | 374790b1 | \([1, 1, 0, -15318, 405972]\) | \(13344095003959/5256576000\) | \(156598655616000\) | \([2]\) | \(1536000\) | \(1.4222\) | \(\Gamma_0(N)\)-optimal |
374790.b2 | 374790b2 | \([1, 1, 0, 49162, 2998068]\) | \(441076027919561/383818500000\) | \(-11434336933500000\) | \([2]\) | \(3072000\) | \(1.7688\) |
Rank
sage: E.rank()
The elliptic curves in class 374790b have rank \(1\).
Complex multiplication
The elliptic curves in class 374790b do not have complex multiplication.Modular form 374790.2.a.b
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.