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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 149058.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
149058.p1 | 149058er3 | \([1, -1, 0, -1941966441, -32939069067059]\) | \(-1956469094246217097/36641439744\) | \(-15168701749244244227260416\) | \([]\) | \(125411328\) | \(3.9562\) | |
149058.p2 | 149058er2 | \([1, -1, 0, -9056826, -100460689484]\) | \(-198461344537/10417365504\) | \(-4312546435048768150381056\) | \([]\) | \(41803776\) | \(3.4069\) | |
149058.p3 | 149058er1 | \([1, -1, 0, 1004589, 3685017181]\) | \(270840023/14329224\) | \(-5931964646386592768136\) | \([]\) | \(13934592\) | \(2.8576\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 149058.p have rank \(1\).
Complex multiplication
The elliptic curves in class 149058.p do not have complex multiplication.Modular form 149058.2.a.p
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.